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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="topgrp_1.html#V3" target="_self">UnContinuous</a> <a href="topgrp_1.html#NM2">TopGroup</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:81"/>
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:81"/><i><font color="Green">E42</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a>,<a class="ref" href="topgrp_1.html#D3" target="_self">TOPGRP_1:def 3</a><br/>

<b>thus </b><a NAME="E3:81"/>
 <a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="topgrp_1.html#D6" target="_self">Def6</a></i>;<br/>

 <a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K2">"</a> 
<b>by </b><i><a class="ref" href="topgrp_1.html#T14" target="_self">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tops_2.html#K2">/"</a> 
<b>by </b><i><a class="txt" href="topgrp_1.html#E2:81"><i><font color="Green">E42</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E5:81"/>
<span class="p1">(<span class="default"><a href="topgrp_1.html#K5" target="_self">inverse_op</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tops_2.html#K2">/"</a>  is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="topgrp_1.html#D6" target="_self">Def6</a></i>;<br/>


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