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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c1">T</font>  st <font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> holds <br/><font color="Olive" title="b1">f</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> implies <font color="Maroon" title="c2">f</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> )</span><br/>



<b>assume </b><a NAME="E1:49"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a></span><br/>

<a NAME="E2:49"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
;<br/>
<a NAME="E3:49"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<b>then </b><font color="Maroon" title="c2">f</font> = 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 

<br/>.= 
 <a href="topgrp_1.html#K4" title="TOPGRP_1:func.4">id</a> <font color="Maroon" title="c1">T</font>
<b>by </b><i><a class="txt" href="#E1:49"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="relat_1.html#T81" title="RELAT_1:th.81">RELAT_1:81</a></i>
;<br/>
<b>hence </b><a NAME="E5:49"/>
<font color="Maroon" title="c2">f</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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