<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c10">S</font>, <font color="Maroon" title="c11">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/>

<b>given </b><font color="Maroon" title="c12">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c10">S</font>,<font color="Maroon" title="c11">T</font><b> such that </b><a NAME="E2:20"/><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c12">f</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 ;<br/>

<a NAME="E3:20"/>
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c12">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c11">T</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c12">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c10">S</font> )
 
<b>by </b><i><a class="txt" href="topreal2.html#E2:20"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:20"/>
( <font color="Maroon" title="c10">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> iff <font color="Maroon" title="c11">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 <b>by </b><i><a class="txt" href="topreal2.html#E35"><i><font color="Green" title="E34">Lm28</font></i></a>, <a class="txt" href="topreal2.html#E36"><i><font color="Green" title="E35">Lm29</font></i></a></i>;<br/>


</div>
