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

<b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A0</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X0</font>;<br/><b>assume </b><a NAME="E1:40_1_1_1"/>
<font color="Maroon">A0</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/><b>then consider </b><font color="Maroon">A</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:40_1_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E4:40_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">A0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X0</font></span>)</span>
 <b>by </b><i><a class="ref" href="tops_2.html#T32">TOPS_2:32</a></i>;<br/><a NAME="E5:40_1_1_1"/>
<font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="tdlat_3.html#E3:40_1_1_1"><i><font color="Green">E21</font></i></a>, </i>;<br/><b>hence </b><a NAME="E6:40_1_1_1"/>
<font color="Maroon">A0</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#T7" target="_self">Th7</a>, <a class="ref" href="pre_topc.html#T43">PRE_TOPC:43</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:40_1_1"/>
<font color="Maroon">X0</font> is <a href="tdlat_3.html#V3" target="_self">almost_discrete</a>
 <b>by </b><i/>;<br/>


</div>
