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<b>set </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> : ( <font color="Olive">x</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">x</font> is <a href="pre_topc.html#V4">closed</a> ) </span>}</span> ;<br/>
<a NAME="E1:2_1_1"/>
(  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> is <a href="pre_topc.html#V3">open</a> &amp;  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> is <a href="pre_topc.html#V4">closed</a> )
 
<b>by </b><i><a class="ref" href="tops_1.html#T22">TOPS_1:22</a>, <a class="ref" href="tops_1.html#T52">TOPS_1:52</a></i>;<br/>
<a NAME="E2:2_1_1"/><b>then </b>
 <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> : ( <font color="Olive">x</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">x</font> is <a href="pre_topc.html#V4">closed</a> ) </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E3:2_1_1"/>
not  <a href="lopclset.html#K1" target="_self">OpenClosedSet</a> <font color="Maroon">T</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


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