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<span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  implies <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V3" title="TOPS_1:attr.3">nowhere_dense</a>  )</span><br/>

<span class="lab"><font color="Green" title="E40">A1</font></span>: <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">TS</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  = 
<span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">TS</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T52" title="PRE_TOPC:th.52">PRE_TOPC:52</a></span>
<br/>.= 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">TS</font>

;<br/>
<span class="kw">assume </span><a NAME="E2:106_1_1"/>
<font color="Maroon" title="c2">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V3" title="TOPS_1:attr.3">nowhere_dense</a> </span><br/>

<span class="kw">hence </span><a NAME="E3:106_1_1"/>
<span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font></span>)</span> <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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_1_1"><span class="lab"><font color="Green" title="E40">A1</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tops_1.html#D4" target="_self" title="TOPS_1:def.4">TOPS_1:def 4</a>,<a class="ref" href="tops_1.html#D5" target="_self" title="TOPS_1:def.5">TOPS_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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