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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: RUSUB_7:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">U</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="normsp_2.html#K3" title="NORMSP_2:func.3">TopSpaceNorm</a> <span class="p2">(<span class="default"><a href="dualsp04.html#K2" title="DUALSP04:func.2">RUSp2RNSp</a> <font color="Olive" title="b1">S</font></span>)</span></span>)</span>  st <font color="Olive" title="b2">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">V</font> holds <br/>( <font color="Olive" title="b2">U</font> is  <a href="dualsp04.html#V2" title="DUALSP04:attr.2">closed</a>  iff <font color="Olive" title="b3">V</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )</div></div>
