<?xml version="1.0"?>
<div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c1">e</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>, <font color="Maroon" title="c2">tE</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">E</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span>)</span> as   <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">O</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c4">X</font></span>)</span>  ex <font color="Olive" title="b2">B</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font> st <br/>( <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Olive" title="b1">O</font></span>)</span></span>)</span> &amp;  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> &amp; ( for <font color="Olive" title="b3">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">O</font> holds <br/> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b3">o</font> #) ) &amp; ( for <font color="Olive" title="b3">T</font> being  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> &amp; ( for <font color="Olive" title="b4">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">O</font> holds <br/><font color="Olive" title="b3">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b4">o</font> #) ) holds <br/><font color="Olive" title="b3">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">B</font> #) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">O</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c4">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">B</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font> st <br/>( <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span></span>)</span> &amp;  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> &amp; ( for <font color="Olive" title="b2">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">o</font> #) ) &amp; ( for <font color="Olive" title="b2">T</font> being  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> &amp; ( for <font color="Olive" title="b3">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/><font color="Olive" title="b2">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b3">o</font> #) ) holds <br/><font color="Olive" title="b2">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">B</font> #) ) )</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c6">B</font> =  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span></span>)</span> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">B</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span></span>)</span> &amp;  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> &amp; ( for <font color="Olive" title="b1">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">o</font> #) ) &amp; ( for <font color="Olive" title="b1">T</font> being  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> &amp; ( for <font color="Olive" title="b2">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">o</font> #) ) holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) ) )</span><br/>

<span class="kw">thus </span><a NAME="E4:58"/>
<font color="Maroon" title="c6">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> &amp; ( for <font color="Olive" title="b1">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">o</font> #) ) &amp; ( for <font color="Olive" title="b1">T</font> being  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> &amp; ( for <font color="Olive" title="b2">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">o</font> #) ) holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">dT</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c2">tE</font> #) as   <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#D1" title="TDLAT_3:def.1">TDLAT_3:def 1</a>, <a class="ref" href="zfmisc_1.html#T1" title="ZFMISC_1:th.1">ZFMISC_1:1</a></span>;<br/>
<a NAME="E6:58"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
 <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <font color="Maroon" title="c2">tE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#T11" title="YELLOW_9:th.11">YELLOW_9:11</a></span>;<br/>
<a NAME="E7:58"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">tE</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T69" title="ENUMSET1:th.69">ENUMSET1:69</a></span>;<br/>
<a NAME="E8:58"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
 <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <font color="Maroon" title="c2">tE</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#T11" title="YELLOW_9:th.11">YELLOW_9:11</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E36">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:58_1"/><span class="lab"><font color="Green" title="E37">A5</font></span>: 
<font color="Maroon" title="c4">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( (  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">e</font> or  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">tE</font> ) &amp;  <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c3">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c7">dT</font> &amp;  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> )</span><br/><span class="kw">hence </span><a NAME="E2:58_1"/><span class="lab"><font color="Green" title="E38">A6</font></span>: 
(  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">e</font> or  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">tE</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T1" title="ZFMISC_1:th.1">ZFMISC_1:1</a>, <a class="ref" href="zfmisc_1.html#T39" title="ZFMISC_1:th.39">ZFMISC_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c3">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c7">dT</font> &amp;  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> )</span><br/><span class="kw">thus </span><a NAME="E3:58_1"/>
 <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c3">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c7">dT</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#T17" title="YELLOW_9:th.17">YELLOW_9:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a></span><br/><span class="kw">hence </span><a NAME="E4:58_1"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:58"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="txt" href="#E7:58"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="txt" href="#E1:58_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="txt" href="#E2:58_1"><span class="lab"><font color="Green" title="E38">A6</font></span></a>, <a class="ref" href="yellow_9.html#T11" title="YELLOW_9:th.11">YELLOW_9:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E10:58"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cantor_1.html#T17" title="CANTOR_1:th.17">CANTOR_1:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/> <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">o</font> #) ) &amp; ( for <font color="Olive" title="b1">T</font> being  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> &amp; ( for <font color="Olive" title="b2">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">o</font> #) ) holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">TT</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) as   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:58"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="cantor_1.html#T17" title="CANTOR_1:th.17">CANTOR_1:17</a></span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> &amp; ( for <font color="Olive" title="b2">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b2">o</font> #) ) holds <br/><font color="Olive" title="b1">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #)</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c9">o</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> implies  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c9">o</font> #) )</span><br/><span class="kw">set </span><font color="Maroon" title="c10">S</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c9">o</font> #);<br/><a NAME="E1:58_2"/><span class="lab"><font color="Green" title="E37">A7</font></span>: 
 <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cantor_1.html#T1" title="CANTOR_1:th.1">CANTOR_1:1</a></span>;<br/><span class="kw">assume </span><a NAME="E2:58_2"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c9">o</font> #)</span><br/><a NAME="E3:58_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A8</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></span>;<br/><a NAME="E4:58_2"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cantor_1.html#T4" title="CANTOR_1:th.4">CANTOR_1:4</a></span>;<br/><a NAME="E5:58_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_2"><span class="lab"><font color="Green" title="E38">A8</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E6:58_2"/><span class="kw">then </span>
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c9">o</font> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c8">TT</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_2"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:58_2"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c9">o</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#D5" title="YELLOW_9:def.5">YELLOW_9:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c9">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c9">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> &amp; ( for <font color="Olive" title="b1">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/><font color="Maroon" title="c9">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">o</font> #) ) implies <font color="Maroon" title="c9">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E13:58"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c9">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font>
 <span class="kw">and </span><br/><a NAME="E14:58"/><span class="lab"><font color="Green" title="E38">A10</font></span>: 
for <font color="Olive" title="b1">o</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> holds <br/><font color="Maroon" title="c9">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Olive" title="b1">o</font> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #)</span><br/>

<span class="kw">thus </span><a NAME="E15:58"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c9">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E37">A9</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="yellow_9.html#D5" title="YELLOW_9:def.5">YELLOW_9:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font></span><br/>

<a NAME="E16:58"/><span class="lab"><font color="Green" title="E39">A11</font></span>: 
( <font color="Maroon" title="c4">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  not <font color="Maroon" title="c9">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E37">A9</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font> implies <font color="Maroon" title="c10">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font> )</span><br/><span class="kw">assume </span><a NAME="E1:58_3"/><span class="lab"><font color="Green" title="E40">A12</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">O</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">o</font> = <font color="Maroon" title="c10">a</font> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c4">X</font> ;<br/><a NAME="E3:58_3"/>
<font color="Maroon" title="c9">T</font> is    <a href="yellow_9.html#M2" title="YELLOW_9:mode.2">TopExtension</a> of  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c11">o</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:58"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="txt" href="#E1:58_3"><span class="lab"><font color="Green" title="E40">A12</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:58_3"/>
<font color="Maroon" title="c10">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#D5" title="YELLOW_9:def.5">YELLOW_9:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E18:58"/><span class="kw">then </span>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T94" title="ZFMISC_1:th.94">ZFMISC_1:94</a></span>;<br/>
<a NAME="E19:58"/><span class="kw">then </span>
 <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c5">O</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="cantor_1.html#T16" title="CANTOR_1:th.16">CANTOR_1:16</a></span>;<br/>
<a NAME="E20:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A13</font></span>: 
<font color="Maroon" title="c6">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="cantor_1.html#T9" title="CANTOR_1:th.9">CANTOR_1:9</a></span>;<br/>
<a NAME="E21:58"/>
<font color="Maroon" title="c4">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="pre_topc.html#D1" title="PRE_TOPC:def.1">PRE_TOPC:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:58"/>
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c6">B</font> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c9">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="txt" href="#E8:58"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="txt" href="#E7:58"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="txt" href="#E9:58"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="txt" href="#E20:58"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="txt" href="#E16:58"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="ref" href="cantor_1.html#T7" title="CANTOR_1:th.7">CANTOR_1:7</a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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