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

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>set </b><font color="Maroon">A1</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">A2</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">A3</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="rcomp_1.html#K2">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a>, <font color="Olive">b</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b</font> &amp; <font color="Olive">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span> ;<br/>
<b>reconsider </b><font color="Maroon">B</font> = <span class="p1">(<span class="default"><span class="p2">{<span class="default"> <span class="p3"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="rcomp_1.html#K2">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a>, <font color="Olive">b</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b</font> &amp; <font color="Olive">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  as    <a href="cantor_1.html#M1">Basis</a> of  <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topmetr.html#K5">I[01]</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:90_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 ;<br/><b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">a</font>, <font color="Maroon">y</font> = <font color="Maroon">b</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/><b>assume </b><a NAME="E3:90_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 ;<br/><a NAME="E4:90_1"/><b>then </b>
( <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Maroon">y</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  &amp; <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">x</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span>  )
 ;<br/><a NAME="E5:90_1"/><b>then </b>
( <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Maroon">y</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span>  &amp; <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">x</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E6:90_1"/><b>then </b>
( <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Maroon">y</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">x</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E7:90_1"/>
( <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> is <a href="pre_topc.html#V3">open</a> )
 <b>by </b><i><a class="ref" href="topgen_5.html#T9" target="_self">Th9</a>, <a class="ref" href="yellow_9.html#T34">YELLOW_9:34</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:90"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b</font> &amp; <font color="Olive">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 holds <br/>( <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">b</font></span><a href="rcomp_2.html#K1">.[</a></span> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/><b>assume </b><a NAME="E1:90_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:90_2"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span>  or <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="rcomp_1.html#K2">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a>, <font color="Olive">b</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b</font> &amp; <font color="Olive">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:90_2_1"/>
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  or <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span>  or <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="rcomp_1.html#K2">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a>, <font color="Olive">b</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b</font> &amp; <font color="Olive">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span>  )
 </span><b>by </b><i><a class="ref" href="topgen_5.html#T10" target="_self">Th10</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_1"><b>suppose </b></a><a NAME="E1:90_2_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span> 
 ;<br/><div class="add"><a NAME="E2:90_2_1_1"/><b>then </b>
 ex <font color="Olive">a</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Olive">a</font></span><a href="rcomp_2.html#K1">.[</a></span> &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 ;<br/><b>hence </b><a NAME="E3:90_2_1_1"/>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="topgen_5.html#T9" target="_self">Th9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_2"><b>suppose </b></a><a NAME="E1:90_2_1_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 ) </span>}</span> 
 ;<br/><div class="add"><a NAME="E2:90_2_1_2"/><b>then </b>
 ex <font color="Olive">a</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Olive">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 ;<br/><b>hence </b><a NAME="E3:90_2_1_2"/>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="topgen_5.html#T9" target="_self">Th9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="90_2_1_3"><b>suppose </b></a><a NAME="E1:90_2_1_3"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="rcomp_1.html#K2">.[</a></span> where <font color="Olive">a</font> is   <a href="real_1.html#NM1">Real</a>, <font color="Olive">b</font> is   <a href="real_1.html#NM1">Real</a> : ( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b</font> &amp; <font color="Olive">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 ) </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">b</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:90_2_1_3"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 ;<br/><a NAME="E4:90_2_1_3"/>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i><a class="ref" href="topgen_5.html#T11" target="_self">Th11</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>then reconsider </b><font color="Maroon">U</font> = <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span>, <font color="Maroon">V</font> = <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span> as  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> <b>by </b><i><a class="ref" href="topgen_5.html#T9" target="_self">Th9</a>, <a class="ref" href="topgen_5.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E6:90_2_1_3"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default">0,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,1</span><a href="rcomp_2.html#K2">.]</a></span>
 <b>by </b><i><a class="ref" href="topgen_5.html#T11" target="_self">Th11</a>, </i>;<br/><a NAME="E7:90_2_1_3"/><b>then </b>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">U</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T137">FUNCT_1:137</a></i>;<br/><b>hence </b><a NAME="E8:90_2_1_3"/>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T38">TOPS_1:38</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:90"/>
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="yellow_9.html#T34">YELLOW_9:34</a></i>;<br/>


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