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<b>let </b><font color="Maroon">c<sub>22</sub></font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/>

<b>consider </b><font color="Maroon">c<sub>23</sub></font> being    <a href="topgrp_1.html#M1">Homeomorphism</a> of  <a href="euclid.html#K15">TOP-REAL</a> 2<b> such that </b><br/><a NAME="E2:153"/><i><font color="Green">E176</font></i>: 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,0</span><a href="euclid.html#K23">]|</a></span> <a href="jordan24.html#R1">realize-max-dist-in</a> <font color="Maroon">c<sub>23</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="ref" href="jordan24.html#T7">JORDAN24:7</a></i>;<br/>
<a NAME="E3:153"/><i><font color="Green">E177</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is    <a href="topgrp_1.html#M1">Homeomorphism</a> of  <a href="euclid.html#K15">TOP-REAL</a> 2
 
<b>by </b><i><a class="ref" href="topgrp_1.html#T30">TOPGRP_1:30</a></i>;<br/>
<a NAME="E4:153"/>
<font color="Maroon">c<sub>23</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>22</sub></font> is   <a href="topreal2.html#NM1">Simple_closed_curve</a>
 
<b>by </b><i><a class="ref" href="jordan.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E5:153"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>22</sub></font> is <a href="jordan1.html#V2">Jordan</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E2:153"><i><font color="Green">E176</font></i></a>, <a class="txt" href="jordan.html#E199"><i><font color="Green">Lemma174</font></i></a></i>;<br/>
<a NAME="E6:153"/><b>then </b><i><font color="Green">E178</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>23</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>23</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> is <a href="jordan1.html#V2">Jordan</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E3:153"><i><font color="Green">E177</font></i></a>, <a class="ref" href="jordan24.html#T16">JORDAN24:16</a></i>;<br/>
<a NAME="E7:153"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E8:153"/><b>then </b><i><font color="Green">E179</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> <a href="funct_1.html#K2">"</a> 
 
<b>by </b><i><a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E9:153"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E10:153"/>
<font color="Maroon">c<sub>22</sub></font> is <a href="jordan1.html#V2">Jordan</a>
 <b>by </b><i><a class="txt" href="jordan.html#E6:153"><i><font color="Green">E178</font></i></a>, <a class="txt" href="jordan.html#E8:153"><i><font color="Green">E179</font></i></a>, <a class="ref" href="jgraph_6.html#T22">JGRAPH_6:22</a></i>;<br/>


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