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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c22">C</font> is  <a href="jordan1.html#V1" title="JORDAN1:attr.1">Jordan</a> </span><br/>

<span class="kw">consider </span><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<span class="kw"> such that </span><br/><a NAME="E2:150"/><span class="lab"><font color="Green" title="E181">A1</font></span>: 
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</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#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</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#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan24.html#T7" title="JORDAN24:th.7">JORDAN24:7</a></span>;<br/>
<a NAME="E3:150"/><span class="lab"><font color="Green" title="E182">A2</font></span>: 
<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
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#T30" title="TOPGRP_1:th.30">TOPGRP_1:30</a></span>;<br/>
<a NAME="E4:150"/>
<font color="Maroon" title="c23">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c22">C</font> is   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan.html#T70" target="_self" title="JORDAN:th.70">Th70</a></span>;<br/>
<a NAME="E5:150"/><span class="kw">then </span>
<font color="Maroon" title="c23">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c22">C</font> is  <a href="jordan1.html#V1" title="JORDAN1:attr.1">Jordan</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:150"><span class="lab"><font color="Green" title="E181">A1</font></span></a>, <a class="txt" href="jordan.html#E205"><span class="lab"><font color="Green" title="E179">Lm91</font></span></a></span>;<br/>
<a NAME="E6:150"/><span class="kw">then </span><span class="lab"><font color="Green" title="E183">A3</font></span>: 
<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#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c22">C</font></span>)</span> is  <a href="jordan1.html#V1" title="JORDAN1:attr.1">Jordan</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:150"><span class="lab"><font color="Green" title="E182">A2</font></span></a>, <a class="ref" href="jordan24.html#T16" title="JORDAN24:th.16">JORDAN24:16</a></span>;<br/>
<a NAME="E7:150"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>;<br/>
<a NAME="E8:150"/><span class="kw">then </span><span class="lab"><font color="Green" title="E184">A4</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></span>;<br/>
<a NAME="E9:150"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:150"/>
<font color="Maroon" title="c22">C</font> is  <a href="jordan1.html#V1" title="JORDAN1:attr.1">Jordan</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:150"><span class="lab"><font color="Green" title="E183">A3</font></span></a>, <a class="txt" href="#E8:150"><span class="lab"><font color="Green" title="E184">A4</font></span></a>, <a class="ref" href="funct_1.html#T107" title="FUNCT_1:th.107">FUNCT_1:107</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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