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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: DUALSP04:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">M</font> being    <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">N</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <font color="Olive" title="b2">M</font></span>)</span> holds <br/>( <font color="Olive" title="b3">N</font> is  <a href="rlsub_1.html#V1" title="RLSUB_1:attr.1">linearly-closed</a>  &amp; <font color="Olive" title="b3">N</font> is  <a href="dualsp04.html#V2" title="DUALSP04:attr.2">closed</a>  )</div></div>
