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

<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<a NAME="E1:94"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">X</font> is <a href="pre_topc.html#V5">continuous</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1"><b>proof </b></a><div class="add">

<a NAME="E1:94_1"/>
for <font color="Olive">V</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">V</font> is <a href="pre_topc.html#V3">open</a> holds <br/><span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">X</font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Olive">V</font> is <a href="pre_topc.html#V3">open</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">V</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><a NAME="E1:94_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">X</font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">V</font> = 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">V</font>
<b>by </b><i><a class="ref" href="grcat_1.html#D11">GRCAT_1:def 11</a></i>
<br/>.= 
<font color="Maroon">V</font>
<b>by </b><i><a class="ref" href="borsuk_1.html#T4">BORSUK_1:4</a></i>
;<br/>
<b>hence </b><a NAME="E3:94_1_1"/>
<span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">X</font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:94_1"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">X</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="tops_2.html#T55">TOPS_2:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:94"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">X</font> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">X</font>
 ;<br/>


</div>
