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<span class="kw">let </span><font color="Maroon" title="c1">FT</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font> holds <br/> ( <font color="Olive" title="b1">P</font> is  <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a>  iff <font color="Olive" title="b1">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="fin_topo.html#V2" title="FIN_TOPO:attr.2">open</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">P</font> is  <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a>  iff <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="fin_topo.html#V2" title="FIN_TOPO:attr.2">open</a>  )</span><br/>



<a NAME="E1:20"/>
( <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="fin_topo.html#V2" title="FIN_TOPO:attr.2">open</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fin_topo.html#T30" title="FIN_TOPO:th.30">FIN_TOPO:30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:20"/>
( <font color="Maroon" title="c2">P</font> is  <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a>  iff <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="fin_topo.html#V2" title="FIN_TOPO:attr.2">open</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fin_topo.html#T31" title="FIN_TOPO:th.31">FIN_TOPO:31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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