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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:71"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">X0</font> being   <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>  holds not <font color="Olive">X0</font> is <a href="tex_3.html#V4" target="_self">nowhere_dense</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>consider </b><font color="Maroon">X0</font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:71_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T10">TSEP_1:10</a></i>;<br/><a NAME="E3:71_1"/>
not <font color="Maroon">X0</font> is <a href="tex_3.html#V4" target="_self">nowhere_dense</a>
 <b>by </b><i><a class="ref" href="tex_3.html#T8" target="_self">Th8</a></i>;<br/><b>hence </b><a NAME="E4:71_1"/>
not <font color="Maroon">A</font> is <a href="tops_1.html#V3">nowhere_dense</a>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:71"/>
<font color="Maroon">X</font> is <a href="tdlat_3.html#V3">almost_discrete</a>
 <b>by </b><i><a class="ref" href="tex_1.html#D7">TEX_1:def 7</a></i>;<br/>


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