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<b>thus </b><a NAME="E1:4_1_1"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font> is <a href="t_0topsp.html#V1">open</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="t_0topsp.html#D2">T_0TOPSP:def 2</a><br/>

<b>assume </b><a NAME="E1:4_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<a NAME="E2:4_1_1_1"/>
<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">T</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T162">FUNCT_1:162</a></i>;<br/>
<b>hence </b><a NAME="E3:4_1_1_1"/>
<span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, <a class="ref" href="grcat_1.html#D11">GRCAT_1:def 11</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">V</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_topc.html#D12">PRE_TOPC:def 12</a><br/>

<b>assume </b><a NAME="E2:4_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">V</font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>

<span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</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">T</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="E4:4_1_1"/>
<span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">V</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i/>;<br/>


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