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<b>let </b><font color="Maroon">S</font> be  <a href="compts_1.html#V3">Hausdorff</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>



<b>assume </b><a NAME="E1:80"/>
for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> holds  <font color="Olive">a</font> <a href="waybel_1.html#K4">"/\"</a>  is <a href="pre_topc.html#V5">continuous</a>
 ;<br/>

<a NAME="E2:80"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a>  is <a href="pre_topc.html#V5">continuous</a>
 
;<br/>
<a NAME="E3:80"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:80"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="ref" href="pcomps_1.html#T10">PCOMPS_1:10</a></i>;<br/>
<b>hence </b><a NAME="E5:80"/>
 <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="waybel_9.html#E3:80"><i><font color="Green">E34</font></i></a>, , <a class="ref" href="pre_topc.html#D12">PRE_TOPC:def 12</a></i>;<br/>


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