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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>let </b><font color="Maroon">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:55"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">X1</font> is <a href="tex_3.html#V4" target="_self">nowhere_dense</a> &amp; <font color="Maroon">X2</font> is <a href="tex_3.html#V4" target="_self">nowhere_dense</a> )
 ;<br/>

<b>reconsider </b><font color="Maroon">A1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<a NAME="E4:55"/>
( <font color="Maroon">A1</font> is <a href="tops_1.html#V3">nowhere_dense</a> &amp; <font color="Maroon">A2</font> is <a href="tops_1.html#V3">nowhere_dense</a> )
 
<b>by </b><i><a class="ref" href="tex_3.html#T8" target="_self">Th8</a>, </i>;<br/>
<a NAME="E5:55"/><b>then </b>
<font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> is <a href="tops_1.html#V3">nowhere_dense</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T90">TOPS_1:90</a></i>;<br/>
<a NAME="E6:55"/><b>then </b>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span> holds <br/><font color="Olive">A</font> is <a href="tops_1.html#V3">nowhere_dense</a>
 
<b>by </b><i><a class="ref" href="tsep_1.html#D2">TSEP_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:55"/>
<font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> is <a href="tex_3.html#V4" target="_self">nowhere_dense</a>
 <b>by </b><i/>;<br/>


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