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<b>let </b><font color="Maroon">T</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:51"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">T</font> is <a href="struct_0.html#V3">empty</a>
 ;<br/>

<a NAME="E2:51"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<a NAME="E3:51"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">f</font> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>
<br/>.= 
 <a href="topgrp_1.html#K4" target="_self">id</a> <font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="topgrp_1.html#T2" target="_self">Th2</a>, <a class="ref" href="relat_1.html#T81">RELAT_1:81</a>, <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E5:51"/>
<font color="Maroon">f</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 ;<br/>


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