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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>;<br/><b>let </b><font color="Maroon" title="c23">h</font> be    <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;<br/>



<b>consider </b><font color="Maroon" title="c24">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <a href="topreal1.html#K2" title="TOPREAL1:func.2">R^2-unit_square</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c22">C</font></span>)</span><b> such that </b><br/><a NAME="E2:110"/><i><font color="Green" title="E130">A1</font></i>: 
<font color="Maroon" title="c24">f</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 <b>by </b><i><a class="ref" href="topreal2.html#D1" title="TOPREAL2:def.1">TOPREAL2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c25">g</font> = <font color="Maroon" title="c23">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c22">C</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c22">C</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">h</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c22">C</font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="jordan24.html#T12" title="JORDAN24:th.12">JORDAN24:12</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c25">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c24">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="topreal2.html#D1" title="TOPREAL2:def.1">TOPREAL2:def 1</a><br/>

<a NAME="E4:110"/>
<font color="Maroon" title="c25">g</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 
<b>by </b><i><a class="ref" href="jordan24.html#T14" title="JORDAN24:th.14">JORDAN24:14</a></i>;<br/>
<b>hence </b><a NAME="E5:110"/>
<font color="Maroon" title="c25">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c24">f</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 <b>by </b><i><a class="txt" href="jordan.html#E2:110"><i><font color="Green" title="E130">A1</font></i></a>, <a class="ref" href="tops_2.html#T71" title="TOPS_2:th.71">TOPS_2:71</a></i>;<br/>


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