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

<b>set </b><font color="Maroon">E</font> =  <a href="openlatt.html#K1">Topology_of</a> <font color="Maroon">T</font>;<br/>
<b>thus </b><a NAME="E1:102_1_1"/>
 <a href="openlatt.html#K1">Topology_of</a> <font color="Maroon">T</font> is <a href="tops_2.html#V1">open</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="102_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="tops_2.html#D1">TOPS_2:def 1</a><br/>

<b>assume </b><a NAME="E1:102_1_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K1">Topology_of</a> <font color="Maroon">T</font>
 ;<br/>

<b>hence </b><a NAME="E2:102_1_1_1"/>
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="openlatt.html#T3">OPENLATT:3</a></i>;<br/>


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

<a NAME="E2:102_1_1"/>
 <a href="openlatt.html#K1">Topology_of</a> <font color="Maroon">T</font> is <a href="topgen_4.html#V1" target="_self">all-open-containing</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="102_1_1_2"><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="topgen_4.html#D2" target="_self">TOPGEN_4:def 2</a><br/>

<b>assume </b><a NAME="E1:102_1_1_2"/>
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>hence </b><a NAME="E2:102_1_1_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K1">Topology_of</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="openlatt.html#T3">OPENLATT:3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:102_1_1"/>
 <a href="openlatt.html#K1">Topology_of</a> <font color="Maroon">T</font> is <a href="topgen_4.html#V1" target="_self">all-open-containing</a>
 ;<br/>


</div>
