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<b>let </b><font color="Maroon" title="c1">TS</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:96"/><i><font color="Green" title="E53">A1</font></i>: 
<font color="Maroon" title="c2">P</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E2:96"/><i><font color="Green" title="E54">A2</font></i>: 
<font color="Maroon" title="c2">P</font> is <a href="tops_1.html#V3" title="TOPS_1:attr.3">nowhere_dense</a>
 <b>and </b><br/><a NAME="E3:96"/><i><font color="Green" title="E55">A3</font></i>: 
<font color="Maroon" title="c2">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E4:96"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a>
 
<b>by </b><i><a class="txt" href="tops_1.html#E2:96"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="tops_1.html#T91" target="_self" title="TOPS_1:th.91">Th91</a></i>;<br/>
<a NAME="E5:96"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="tops_1.html#E1:96"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="tops_1.html#E3:96"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="tops_1.html#T80" target="_self" title="TOPS_1:th.80">Th80</a></i>;<br/>
<b>hence </b><a NAME="E6:96"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></i>;<br/>


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