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<b>let </b><font color="Maroon">GX</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/>



<b>assume </b><a NAME="E1:90"/>
( <font color="Maroon">S</font> is <a href="tops_1.html#V2" target="_self">boundary</a> &amp; <font color="Maroon">S</font> is <a href="pre_topc.html#V4">closed</a> )
 ;<br/>

<a NAME="E2:90"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">S</font> is <a href="tops_1.html#V2" target="_self">boundary</a>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>
<b>hence </b><a NAME="E3:90"/>
<font color="Maroon">S</font> is <a href="tops_1.html#V3" target="_self">nowhere_dense</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T45" target="_self">Th45</a></i>;<br/>


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