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

<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">Q</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">R</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM6">Function</a> of <a href="borsuk_1.html#K20">I[01]</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">P</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="borsuk_1.html#K20">I[01]</a> ;<br/>









<b>assume </b><a NAME="E1:10"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">f</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp; <font color="Maroon">F</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1 &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp; <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> &amp; <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font> &amp; <font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">ppi</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">pi1</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:10"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">ppi</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">pi1</font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">ppi</font> &amp; <font color="Maroon">ppi</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">pi1</font> &amp; <font color="Maroon">pi1</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp;  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span><a href="rcomp_1.html#K1">.]</a></span> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">ppi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">pi1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 <b>by </b><i/>;<br/>
<a NAME="E4:10"/>
( <font color="Maroon">ppi</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">dd</font> where <font color="Olive">dd</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">ppi</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">dd</font> &amp; <font color="Olive">dd</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">pi1</font> ) </span>}</span>  &amp; <font color="Maroon">pi1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">dd</font> where <font color="Olive">dd</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">ppi</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">dd</font> &amp; <font color="Olive">dd</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">pi1</font> ) </span>}</span>  )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">Poz</font> = <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span><a href="rcomp_1.html#K1">.]</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="borsuk_1.html#K20">I[01]</a>  <b>by </b><i>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="rcomp_1.html#D1">RCOMP_1:def 1</a>, <a class="ref" href="treal_1.html#T1">TREAL_1:1</a></i>;<br/>
<i><font color="Green">E33</font></i>: the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span> = 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>

<br/>.= 
<font color="Maroon">Poz</font>
<b>by </b><i><a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>
;<br/>
<i><font color="Green">E36</font></i>:  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> = 
 <a href="pre_topc.html#K2">[#]</a> <a href="borsuk_1.html#K20">I[01]</a> 
<b>by </b><i>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>
<br/>.= 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
<b>by </b><i><a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a></i>
;<br/>
<a NAME="E8:10"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E9:10"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Poz</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:10_3"/>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Poz</font>
 <b>by </b><i>, , , , <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="funct_1.html#T157">FUNCT_1:157</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E2:10_3"/>
<font color="Maroon">Poz</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 <b>by </b><i>, , , , <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="funct_1.html#T157">FUNCT_1:157</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">gg</font> = <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">P</font>;<br/>
<b>reconsider </b><font color="Maroon">gg</font> = <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">P</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> <b>by </b><i>, , <a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/>
<b>reconsider </b><font color="Maroon">SEG</font> =  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> <b>by </b><i/>;<br/>
<i><font color="Green">E51</font></i>: the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">SEG</font></span>)</span> = 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">SEG</font></span>)</span>

<br/>.= 
<font color="Maroon">SEG</font>
<b>by </b><i><a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>
;<br/>
<a NAME="E13:10"/><i><font color="Green">E52</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">gg</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">SEG</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">ii</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:10_5"/>
<font color="Maroon">ii</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">gg</font>
 ;<br/>

<b>then consider </b><font color="Maroon">j</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:10_5"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">gg</font> &amp; <font color="Maroon">ii</font> <a href="hidden.html#R1">=</a> <font color="Maroon">gg</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:10_5"/>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Poz</font>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E5:10_5"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:10_5"/><i><font color="Green">E55</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">gg</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Poz</font>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:10_5"/><b>then </b>
( <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">i</font> )
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E8:10_5"/>
<font color="Maroon">ii</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SEG</font>
 <b>by </b><i>, , , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon">SEG</font> = <font color="Maroon">SEG</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> ;<br/>
<a NAME="E15:10"/><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">SEG</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">R</font>
 
<b>by </b><i>, <a class="ref" href="goboard9.html#T4">GOBOARD9:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">hh'</font> = <font color="Maroon">gg</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">SEG</font></span>)</span> <b>by </b><i>, , <a class="ref" href="funct_2.html#T8">FUNCT_2:8</a></i>;<br/>
<a NAME="E17:10"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">F</font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E18:10"/><b>then </b>
<font color="Maroon">gg</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i>, <a class="ref" href="topmetr.html#T10">TOPMETR:10</a></i>;<br/>
<a NAME="E19:10"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">hh'</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="ref" href="topmetr.html#T9">TOPMETR:9</a></i>;<br/>
<a NAME="E20:10"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">hh'</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T84">FUNCT_1:84</a></i>;<br/>
<b>reconsider </b><font color="Maroon">hh</font> = <font color="Maroon">hh'</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">R</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E22:10"/><i><font color="Green">E60</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">hh</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E23:10"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">hh</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Poz</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<i><font color="Green">E62</font></i>:  <a href="relset_1.html#K5">rng</a> <font color="Maroon">hh</font> = 
<font color="Maroon">hh</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">hh</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T45">FUNCT_2:45</a>, </i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">Q</font></span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">SEG</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="rfunct_2.html#T5">RFUNCT_2:5</a>, </i>
;<br/>
<a NAME="E25:10"/><i><font color="Green">E64</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Poz</font>
 
<b>by </b><i>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A</font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> as  <a href="pre_topc.html#V1">strict</a>  <a href="pre_topc.html#M1">SubSpace</a> of  <a href="borsuk_1.html#K20">I[01]</a>  <b>by </b><i>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="treal_1.html#T6">TREAL_1:6</a></i>;<br/>
<a NAME="E27:10"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">Poz</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E28:10"/>
 <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font> is <a href="compts_1.html#V2">compact</a>
 
<b>by </b><i>, <a class="ref" href="heine.html#T11">HEINE:11</a></i>;<br/>
<a NAME="E29:10"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">ppi</font>,<font color="Maroon">pi1</font></span>)</span> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i><a class="ref" href="compts_1.html#T10">COMPTS_1:10</a></i>;<br/>
<a NAME="E30:10"/><b>then </b>
for <font color="Olive">P</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>  st <font color="Olive">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Poz</font> holds <br/><font color="Olive">P</font> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i/>;<br/>
<a NAME="E31:10"/><b>then </b>
<font color="Maroon">Poz</font> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i>, <a class="ref" href="compts_1.html#T11">COMPTS_1:11</a></i>;<br/>
<a NAME="E32:10"/><b>then </b><i><font color="Green">E66</font></i>: 
<a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">Poz</font> is <a href="compts_1.html#V2">compact</a>
 
<b>by </b><i><a class="ref" href="compts_1.html#T12">COMPTS_1:12</a></i>;<br/>
<a NAME="E33:10"/>
<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">R</font> <a href="compts_1.html#NR2" target="_self">is_T2</a> 
 
<b>by </b><i><a class="ref" href="topmetr.html#T3">TOPMETR:3</a></i>;<br/>
<a NAME="E34:10"/><b>then </b>
<font color="Maroon">hh</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i>, , , , , <a class="ref" href="jordan5b.html#T1" target="_self">Th1</a>, <a class="ref" href="compts_1.html#T26">COMPTS_1:26</a></i>;<br/>
<b>hence </b><a NAME="E35:10"/>
 ex <font color="Olive">G</font> being  <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K20">I[01]</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">P</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">R</font></span>)</span> st <br/>( <font color="Olive">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">P</font> &amp; <font color="Olive">G</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a>  )
 <b>by </b><i/>;<br/>


</div>
