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<div>:: <span class="kw">deftheorem </span>   defines <a href="pcomps_1.html#V1" title="PCOMPS_1:attr.1">locally_finite</a> <a onclick="hs(this)" href="javascript:()">PCOMPS_1:def 1 : <br/></a><span> for <font color="Olive" title="b1">T</font> being    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">IT</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Olive" title="b1">T</font> holds <br/> ( <font color="Olive" title="b2">IT</font> is  <a href="pcomps_1.html#V1" title="PCOMPS_1:attr.1">locally_finite</a>  iff  for <font color="Olive" title="b3">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">T</font>  ex <font color="Olive" title="b4">W</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font> st <br/>( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">W</font> &amp; <font color="Olive" title="b4">W</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <span class="p1"> { <span class="default"> <font color="Olive" title="b5">V</font> where <font color="Olive" title="b5">V</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font> : ( <font color="Olive" title="b5">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">IT</font> &amp; <font color="Olive" title="b5">V</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b4">W</font> ) </span> } </span>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) );<br/></span></div>
