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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>consider </b><font color="Maroon" title="c2">x</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E2:8"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <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">T</font>
 ;<br/>
<a NAME="E3:8"/>
<font color="Maroon" title="c2">x</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="txt" href="lopclset.html#E2:8"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="tops_1.html#T53" title="TOPS_1:th.53">TOPS_1:53</a></i>;<br/>
<b>hence </b><a NAME="E4:8"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="lopclset.html#K1" title="LOPCLSET:func.1">OpenClosedSet</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="lopclset.html#E2:8"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="lopclset.html#T4" target="_self" title="LOPCLSET:th.4">Th4</a></i>;<br/>


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