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<b>let </b><font color="Maroon">T</font> be  <a href="topgrp_1.html#V3" target="_self">UnContinuous</a> <a href="topgrp_1.html#NM4">TopGroup</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">a</font> <a href="group_1.html#K3">"</a> ;<br/>





<b>reconsider </b><font color="Maroon">f</font> =  <a href="topgrp_1.html#K6" target="_self">inverse_op</a> <font color="Maroon">T</font> as   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">T</font> ;<br/>
<a NAME="E2:78"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K3">"</a> 
 
<b>by </b><i><a class="ref" href="group_1.html#D7">GROUP_1:def 7</a></i>;<br/>
<a NAME="E3:78"/>
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">H</font> being    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">a</font><b> such that </b><br/><a NAME="E5:78"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W</font>
 <b>by </b><i>, <a class="ref" href="borsuk_1.html#D3">BORSUK_1:def 3</a></i>;<br/>
<a NAME="E6:78"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D1">CONNSP_2:def 1</a></i>;<br/>
<a NAME="E7:78"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tops_1.html#T45">TOPS_1:45</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> =  <a href="tops_1.html#K1">Int</a> <font color="Maroon">H</font> as  <a href="pre_topc.html#V3">open</a>  <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">a</font> <b>by </b><i><a class="ref" href="connsp_2.html#D1">CONNSP_2:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<a NAME="E9:78"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">A</font> <a href="group_2.html#K1">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">g</font> <a href="group_1.html#K3">"</a> </span>)</span> where <font color="Olive">g</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> : <font color="Olive">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="group_2.html#D1">GROUP_2:def 1</a></i>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E10:78"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="group_2.html#K1">"</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">g</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E12:78"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="group_1.html#K3">"</a>  &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="topgrp_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E13:78"/><i><font color="Green">E50</font></i>: 
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T44">TOPS_1:44</a></i>;<br/>
<a NAME="E14:78"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="group_1.html#K3">"</a> 
 
<b>by </b><i><a class="ref" href="group_1.html#D7">GROUP_1:def 7</a></i>;<br/>
<a NAME="E15:78"/><b>then </b>
<font color="Maroon">g</font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">H</font>
 
<b>by </b><i>, , <a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<b>hence </b><a NAME="E16:78"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font>
 <b>by </b><i><a class="txt" href="topgrp_1.html#E5:78"><i><font color="Green">E40</font></i></a>, </i>;<br/>


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