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

<b>let </b><font color="Maroon">T</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:62"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">A</font> is <a href="topgen_1.html#V2" target="_self">dense-in-itself</a> )
 ;<br/>

<b>then </b><font color="Maroon">A</font> = 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
<b>by </b><i><a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topgen_1.html#K2" target="_self">Der</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:62"/>
 <a href="topgen_1.html#K2" target="_self">Der</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E4:62"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="topgen_1.html#K2" target="_self">Der</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="topgen_1.html#T4" target="_self">Th4</a></i>;<br/>


</div>
