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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:74"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="urysohn1.html#V1">being_T1</a>
 ;<br/>

<a NAME="E2:74"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="topgen_1.html#K2">Der</a> <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:74_1"/>
 <a href="topgen_1.html#K2">Der</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2">Der</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E1:74"><i><font color="Green">E39</font></i></a>, <a class="ref" href="topgen_1.html#T35">TOPGEN_1:35</a></i>;<br/>
<b>hence </b><a NAME="E2:74_1"/>
 <a href="topgen_1.html#K2">Der</a> <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:74"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="topgen_4.html#V7" target="_self">T_1/2</a>
 <b>by </b><i><a class="ref" href="topgen_4.html#D8" target="_self">Def8</a></i>;<br/>


</div>
