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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">M</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K5" title="RUSUB_5:func.5">TopUnitSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:51"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">V</font>
 ;<br/>

<a NAME="E2:51"/><b>then </b>
<font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K5" title="RUSUB_5:func.5">TopUnitSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T5" title="PRE_TOPC:th.5">PRE_TOPC:5</a></i>;<br/>
<b>hence </b><a NAME="E3:51"/>
<font color="Maroon" title="c2">M</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="ref" href="pre_topc.html#D5" title="PRE_TOPC:def.5">PRE_TOPC:def 5</a></i>;<br/>

<a NAME="E4:51"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K5" title="RUSUB_5:func.5">TopUnitSpace</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">M</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="txt" href="rusub_5.html#E1:51"><i><font color="Green" title="E30">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:51"/>
<font color="Maroon" title="c2">M</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="ref" href="pre_topc.html#D6" title="PRE_TOPC:def.6">PRE_TOPC:def 6</a></i>;<br/>


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