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<div>:: <span class="kw">deftheorem </span>   defines <a href="compl_sp.html#V3" title="COMPL_SP:attr.3">closed</a> <a onclick="hs(this)" href="javascript:()">COMPL_SP:def 4 : <br/></a><span> for <font color="Olive" title="b1">M</font> being    <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">M</font> holds <br/> ( <font color="Olive" title="b2">A</font> is  <a href="compl_sp.html#V3" title="COMPL_SP:attr.3">closed</a>  iff <font color="Olive" title="b2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="compl_sp.html#V2" title="COMPL_SP:attr.2">open</a>  );<br/></span></div>
