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

<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">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="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">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="c2">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="c1">X</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c3">B</font>
;<br/>

<b>thus </b><a NAME="E2:57"/>
<font color="Maroon" title="c3">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="c2">O</font></span>)</span></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">E</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p1">(<span class="default"><a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <span class="p2">(<span class="default"><a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">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="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">e</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <span class="p1">(<span class="default"><a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>, <font color="Maroon" title="c6">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/>
<b>reconsider </b><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="c6">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>  <b>by </b><i><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></i>;<br/>
<a NAME="E6:57"/><i><font color="Green" title="E33">A1</font></i>: 
(  <a href="cantor_1.html#K1" title="CANTOR_1:func.1">UniCl</a> <font color="Maroon" title="c6">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> &amp;  <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <font color="Maroon" title="c5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">tE</font> )
 
<b>by </b><i><a class="ref" href="yellow_9.html#T11" title="YELLOW_9:th.11">YELLOW_9:11</a>, <a class="ref" href="yellow_9.html#T17" title="YELLOW_9:th.17">YELLOW_9:17</a></i>;<br/>
<a NAME="E7:57"/><i><font color="Green" title="E34">A2</font></i>: 
(  <a href="cantor_1.html#K2" title="CANTOR_1:func.2">FinMeetCl</a> <font color="Maroon" title="c6">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> &amp; <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="c6">tE</font> )
 
<b>by </b><i><a class="ref" href="enumset1.html#T69" title="ENUMSET1:th.69">ENUMSET1:69</a>, <a class="ref" href="yellow_9.html#T11" title="YELLOW_9:th.11">YELLOW_9:11</a></i>;<br/>
<div><i><font color="Green" title="E35">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:57_1"/><i><font color="Green" title="E36">A4</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><b>hence </b><a NAME="E2:57_1"/><i><font color="Green" title="E37">A5</font></i>: 
(  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">e</font> or  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">tE</font> )
 <b>by </b><i><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></i>;<br/><b>thus </b><a NAME="E3:57_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="c4">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>
 <b>by </b><i><a class="ref" href="yellow_9.html#T17" title="YELLOW_9:th.17">YELLOW_9:17</a></i>;<br/><b>hence </b><a NAME="E4:57_1"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>
 <b>by </b><i><a class="txt" href="topgen_2.html#E7:57"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="topgen_2.html#E1:57_1"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="topgen_2.html#E2:57_1"><i><font color="Green" title="E37">A5</font></i></a>, <a class="ref" href="yellow_9.html#T11" title="YELLOW_9:th.11">YELLOW_9:11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:57"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">B</font> #) is   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>
 <b>by </b><i><a class="ref" href="cantor_1.html#T17" title="CANTOR_1:th.17">CANTOR_1:17</a></i>;<br/>

<b>reconsider </b><font color="Maroon" title="c8">TT</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">B</font> #) as   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> <b>by </b><i><a class="txt" href="topgen_2.html#E8:57"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="cantor_1.html#T17" title="CANTOR_1:th.17">CANTOR_1:17</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>let </b><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="c1">X</font>;<br/><b>set </b><font color="Maroon" title="c10">S</font> =  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c9">o</font> #);<br/><b>assume </b><a NAME="E1:57_2"/><i><font color="Green" title="E36">A6</font></i>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font>
 ;<br/><a NAME="E2:57_2"/>
<font color="Maroon" title="c8">TT</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="c1">X</font>,<font color="Maroon" title="c9">o</font> #)
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:57_2_1"/>
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="c1">X</font>,<font color="Maroon" title="c9">o</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 <font color="Maroon" title="c8">TT</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_9.html#D5" title="YELLOW_9:def.5">YELLOW_9:def 5</a><br/>

<a NAME="E2:57_2_1"/>
( <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="c2">O</font> &amp;  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">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="c2">O</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="topgen_2.html#E1:57_2"><i><font color="Green" title="E36">A6</font></i></a>, <a class="ref" href="cantor_1.html#T4" title="CANTOR_1:th.4">CANTOR_1:4</a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E3:57_2_1"/><b>then </b>
( <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="c2">O</font></span>)</span> &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="c2">O</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font> )
 
<b>by </b><i><a class="ref" href="cantor_1.html#T1" title="CANTOR_1:th.1">CANTOR_1:1</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:57_2_1"/>
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="c1">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>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:57_2"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">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="c1">X</font>,<font color="Maroon" title="c9">o</font> #)
 ;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c9">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E12:57"/><i><font color="Green" title="E36">A7</font></i>: 
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="c1">X</font>
 <b>and </b><br/><a NAME="E13:57"/><i><font color="Green" title="E37">A8</font></i>: 
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="c1">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="c2">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="c1">X</font>,<font color="Olive" title="b1">o</font> #)
 ;<br/>

<b>thus </b><a NAME="E14:57"/>
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="c1">X</font>,<font color="Maroon" title="c3">B</font> #)
 <b>by </b><i><a class="txt" href="topgen_2.html#E12:57"><i><font color="Green" title="E36">A7</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_9.html#D5" title="YELLOW_9:def.5">YELLOW_9:def 5</a><br/>

<a NAME="E15:57"/><i><font color="Green" title="E38">A9</font></i>: 
<font color="Maroon" title="c1">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>
 
<b>by </b><i><a class="txt" href="topgen_2.html#E12:57"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="pre_topc.html#D1" title="PRE_TOPC:def.1">PRE_TOPC:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:57_3"/><i><font color="Green" title="E39">A10</font></i>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">O</font>
 ;<br/><b>then reconsider </b><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="c1">X</font> ;<br/><a NAME="E3:57_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="c1">X</font>,<font color="Maroon" title="c11">o</font> #)
 <b>by </b><i><a class="txt" href="topgen_2.html#E13:57"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="topgen_2.html#E1:57_3"><i><font color="Green" title="E39">A10</font></i></a></i>;<br/><b>hence </b><a NAME="E4:57_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>
 <b>by </b><i><a class="ref" href="yellow_9.html#D5" title="YELLOW_9:def.5">YELLOW_9:def 5</a></i>;<br/></div><b>end;</b></div>
<a NAME="E17:57"/><b>then </b>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c2">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>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T94" title="ZFMISC_1:th.94">ZFMISC_1:94</a></i>;<br/>
<a NAME="E18:57"/><b>then </b>
 <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="c2">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>
 
<b>by </b><i><a class="txt" href="topgen_2.html#E12:57"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="cantor_1.html#T16" title="CANTOR_1:th.16">CANTOR_1:16</a></i>;<br/>
<a NAME="E19:57"/><b>then </b><i><font color="Green" title="E39">A11</font></i>: 
<font color="Maroon" title="c3">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>
 
<b>by </b><i><a class="txt" href="topgen_2.html#E12:57"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="cantor_1.html#T9" title="CANTOR_1:th.9">CANTOR_1:9</a></i>;<br/>
<a NAME="E20:57"/>
( <font color="Maroon" title="c1">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> )
 
<b>by </b><i><a class="txt" href="topgen_2.html#E12:57"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E21:57"/>
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="c1">X</font>,<font color="Maroon" title="c3">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>
 <b>by </b><i><a class="txt" href="topgen_2.html#E6:57"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="topgen_2.html#E7:57"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="topgen_2.html#E8:57"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="topgen_2.html#E15:57"><i><font color="Green" title="E38">A9</font></i></a>, <a class="txt" href="topgen_2.html#E19:57"><i><font color="Green" title="E39">A11</font></i></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></i>;<br/>


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