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<span class="kw">set </span><font color="Maroon" title="c1">X</font> =  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ;<br/>
<a NAME="E1:47_1_1"/>
 <a href="pcomps_1.html#K3" title="PCOMPS_1:func.3">TopSpaceMetr</a> <span class="p1">(<span class="default"><a href="metric_1.html#K5" title="METRIC_1:func.5">DiscreteSpace</a>  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> </span>)</span> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E2:47_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   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> st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="metrizts.html#V1" title="METRIZTS:attr.1">Lindelof</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="pcomps_1.html#V3" title="PCOMPS_1:attr.3">metrizable</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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