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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">R</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/>



<a NAME="E1:8"/>
( <font color="Maroon">R</font> is <a href="pre_topc.html#V4">closed</a> iff <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">GX</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">R</font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#D6">PRE_TOPC:def 6</a></i>;<br/>
<b>hence </b><a NAME="E2:8"/>
( <font color="Maroon">R</font> is <a href="pre_topc.html#V4">closed</a> iff <font color="Maroon">R</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a> )
 ;<br/>


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