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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K23" title="COMPLSP1:func.23">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K8" title="COMPLSP1:func.8">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:106"/><i><font color="Green" title="E67">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font>
 ;<br/>

<a NAME="E2:106"/>
( <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><a href="complsp1.html#K23" title="COMPLSP1:func.23">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> iff <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="complsp1.html#V1" title="COMPLSP1:attr.1">open</a> )
 
<b>by </b><i><a class="txt" href="complsp1.html#E1:106"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="complsp1.html#T108" target="_self" title="COMPLSP1:th.108">Th108</a></i>;<br/>
<b>hence </b><a NAME="E3:106"/>
( <font color="Maroon" title="c3">A</font> is <a href="complsp1.html#V2" title="COMPLSP1:attr.2">closed</a> iff <font color="Maroon" title="c2">V</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 <b>by </b><i><a class="ref" href="complsp1.html#T109" target="_self" title="COMPLSP1:th.109">Th109</a>, <a class="ref" href="pre_topc.html#D6" title="PRE_TOPC:def.6">PRE_TOPC:def 6</a></i>;<br/>


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