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

<b>let </b><font color="Maroon">C</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon">h</font> be    <a href="topgrp_1.html#M3">Homeomorphism</a> of  <a href="euclid.html#K15">TOP-REAL</a> 2;<br/>



<b>consider </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</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> <a href="topreal1.html#K2">R^2-unit_square</a> </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">C</font></span>)</span><b> such that </b><br/><a NAME="E2:110"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">f</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 <b>by </b><i><a class="ref" href="topreal2.html#D1">TOPREAL2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">h</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">C</font> as   <a href="struct_0.html#NM6">Function</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">C</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> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C</font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="jordan24.html#T12">JORDAN24:12</a></i>;<br/>
<b>take </b>
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal2.html#D1">TOPREAL2:def 1</a><br/>

<a NAME="E4:110"/>
<font color="Maroon">g</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="ref" href="jordan24.html#T14">JORDAN24:14</a></i>;<br/>
<b>hence </b><a NAME="E5:110"/>
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 <b>by </b><i>, <a class="ref" href="tops_2.html#T71">TOPS_2:71</a></i>;<br/>


</div>
