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

<b>let </b><font color="Maroon" title="c1">GX</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>;<br/>



<a NAME="E1:74"/>
( <font color="Maroon" title="c2">R</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> iff <font color="Maroon" title="c2">R</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> )
 
<b>by </b><i><a class="ref" href="tops_1.html#D4" target="_self" title="TOPS_1:def.4">Def4</a></i>;<br/>
<a NAME="E2:74"/><b>then </b>
( <font color="Maroon" title="c2">R</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> iff  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">GX</font> )
 
<b>by </b><i><a class="ref" href="tops_1.html#D3" target="_self" title="TOPS_1:def.3">Def3</a></i>;<br/>
<a NAME="E3:74"/><b>then </b>
( <font color="Maroon" title="c2">R</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> iff <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">GX</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 
<b>by </b><i><a class="ref" href="subset_1.html#T64" title="SUBSET_1:th.64">SUBSET_1:64</a></i>;<br/>
<b>hence </b><a NAME="E4:74"/>
( <font color="Maroon" title="c2">R</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> iff  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/>


</div>
