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<b>let </b><font color="Maroon">X</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">Vt</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="normsp_2.html#K3" target="_self">TopSpaceNorm</a> <font color="Maroon">X</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:24"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Vt</font>
 ;<br/>

<a NAME="E2:24"/>
( <font color="Maroon">V</font> is <a href="nfcont_1.html#V3">open</a> iff <font color="Maroon">V</font> <a href="subset_1.html#K3">`</a>  is <a href="nfcont_1.html#V2">closed</a> )
 
<b>by </b><i><a class="ref" href="nfcont_1.html#D6">NFCONT_1:def 6</a></i>;<br/>
<a NAME="E3:24"/><b>then </b>
( <font color="Maroon">V</font> is <a href="nfcont_1.html#V3">open</a> iff <font color="Maroon">Vt</font> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V4">closed</a> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:24"/>
( <font color="Maroon">V</font> is <a href="nfcont_1.html#V3">open</a> iff <font color="Maroon">Vt</font> is <a href="pre_topc.html#V3">open</a> )
 <b>by </b><i><a class="ref" href="tops_1.html#T30">TOPS_1:30</a></i>;<br/>


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