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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: NORMSP_3:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">R</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">R</font> is  <a href="nfcont_1.html#V2" title="NFCONT_1:attr.2">closed</a>  iff <font color="Olive" title="b2">R</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="nfcont_1.html#V3" title="NFCONT_1:attr.3">open</a>  ) ;<br/></div></div>
