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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 <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>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#K4" target="_self">LinearTopSpaceNorm</a> <font color="Maroon">X</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:31"/><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="E2:31"/>
( <font color="Maroon">Vt</font> is <a href="pre_topc.html#V3">open</a> iff <font color="Maroon">Vt</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="normsp_2.html#K4" target="_self">LinearTopSpaceNorm</a> <font color="Maroon">X</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E3:31"/><b>then </b>
( <font color="Maroon">Vt</font> is <a href="pre_topc.html#V3">open</a> iff <font color="Maroon">Vt</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</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> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:31"/>
( <font color="Maroon">V</font> is <a href="pre_topc.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="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>


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