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

<b>thus </b><a NAME="E1:22_1_1"/>
( <font color="Maroon">A</font> is <a href="tops_1.html#V3">nowhere_dense</a> implies  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1"/>
<font color="Maroon">A</font> is <a href="tops_1.html#V3">nowhere_dense</a>
 ;<br/>

<a NAME="E2:22_1_1_1"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> is <a href="tops_1.html#V2">boundary</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#D5">TOPS_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1_1_1"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/>


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

<b>assume </b><a NAME="E2:22_1_1"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:22_1_1"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> is <a href="tops_1.html#V2">boundary</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:22_1_1"/>
<font color="Maroon">A</font> is <a href="tops_1.html#V3">nowhere_dense</a>
 <b>by </b><i><a class="ref" href="tops_1.html#D5">TOPS_1:def 5</a></i>;<br/>


</div>
