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



<b>reconsider </b><font color="Maroon">V0</font> = <font color="Maroon">V</font> as   <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> <b>by </b><i/>;<br/>
<a NAME="E2:33"/>
( <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a> iff <font color="Maroon">V0</font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:33"/>
( <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a> iff for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> holds <br/> ex <font color="Olive">r</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">r</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">{<span class="default"> <font color="Olive">y</font> where <font color="Olive">y</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font> : <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Olive">y</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">r</font> </span>}</span>  <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> ) )
 <b>by </b><i/>;<br/>


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