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<b>let </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/>

<b>given </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font><b> such that </b><a NAME="E1:20"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 ;<br/>

<a NAME="E2:20"/>
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="topreal2.html#E1:20"><i><font color="Green">E37</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon">c<sub>10</sub></font> is <a href="struct_0.html#V3">empty</a> iff <font color="Maroon">c<sub>11</sub></font> is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i><a class="txt" href="topreal2.html#E35"><i><font color="Green">Lemma34</font></i></a>, <a class="txt" href="topreal2.html#E36"><i><font color="Green">Lemma35</font></i></a></i>;<br/>


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