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<b>let </b><font color="Maroon" title="c22">C</font> be   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c22">C</font> is <a href="jordan1.html#V2" title="JORDAN1:attr.2">Jordan</a></span><br/>

<b>consider </b><font color="Maroon" title="c23">f</font> being    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of  <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2<b> such that </b><br/><a NAME="E2:152"/><i><font color="Green" title="E176">A1</font></i>: 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>,<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="jordan24.html#R1" title="JORDAN24:pred.1">realize-max-dist-in</a> <font color="Maroon" title="c23">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="jordan24.html#T7" title="JORDAN24:th.7">JORDAN24:7</a></i>;<br/>
<a NAME="E3:152"/><i><font color="Green" title="E177">A2</font></i>: 
<font color="Maroon" title="c23">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of  <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2
 
<b>by </b><i><a class="ref" href="topgrp_1.html#T30" title="TOPGRP_1:th.30">TOPGRP_1:30</a></i>;<br/>
<a NAME="E4:152"/>
<font color="Maroon" title="c23">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c22">C</font> is   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a>
 
<b>by </b><i><a class="ref" href="jordan.html#T70" target="_self" title="JORDAN:th.70">Th70</a></i>;<br/>
<a NAME="E5:152"/><b>then </b>
<font color="Maroon" title="c23">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c22">C</font> is <a href="jordan1.html#V2" title="JORDAN1:attr.2">Jordan</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E2:152"><i><font color="Green" title="E176">A1</font></i></a>, <a class="txt" href="jordan.html#E199"><i><font color="Green" title="E174">Lm85</font></i></a></i>;<br/>
<a NAME="E6:152"/><b>then </b><i><font color="Green" title="E178">A3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c22">C</font></span>)</span> is <a href="jordan1.html#V2" title="JORDAN1:attr.2">Jordan</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E3:152"><i><font color="Green" title="E177">A2</font></i></a>, <a class="ref" href="jordan24.html#T16" title="JORDAN24:th.16">JORDAN24:16</a></i>;<br/>
<a NAME="E7:152"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c23">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E8:152"/><b>then </b><i><font color="Green" title="E179">A4</font></i>: 
<font color="Maroon" title="c23">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<b>by </b><i><a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E9:152"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c23">f</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 <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E10:152"/>
<font color="Maroon" title="c22">C</font> is <a href="jordan1.html#V2" title="JORDAN1:attr.2">Jordan</a>
 <b>by </b><i><a class="txt" href="jordan.html#E6:152"><i><font color="Green" title="E178">A3</font></i></a>, <a class="txt" href="jordan.html#E8:152"><i><font color="Green" title="E179">A4</font></i></a>, <a class="ref" href="jgraph_6.html#T22" title="JGRAPH_6:th.22">JGRAPH_6:22</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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