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<b>let </b><font color="Maroon">TS</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/><b>let </b><font color="Maroon">Q</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:85"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">P</font> is <a href="tops_1.html#V3" target="_self">nowhere_dense</a>
 <b>and </b><br/><a NAME="E2:85"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">Q</font> is <a href="tops_1.html#V3" target="_self">nowhere_dense</a>
 ;<br/>

<a NAME="E3:85"/><i><font color="Green">E36</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">P</font> is <a href="tops_1.html#V2" target="_self">boundary</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T46" target="_self">Th46</a>, <a class="ref" href="tops_1.html#T45" target="_self">Th45</a></i>;<br/>
<a NAME="E4:85"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> is <a href="tops_1.html#V2" target="_self">boundary</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T47" target="_self">Th47</a>, <a class="ref" href="tops_1.html#T45" target="_self">Th45</a></i>;<br/>
<a NAME="E5:85"/><b>then </b>
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">P</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font></span>)</span> is <a href="tops_1.html#V2" target="_self">boundary</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T48" target="_self">Th48</a>, </i>;<br/>
<a NAME="E6:85"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font></span>)</span> is <a href="tops_1.html#V2" target="_self">boundary</a>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T50">PRE_TOPC:50</a></i>;<br/>
<b>hence </b><a NAME="E7:85"/>
<font color="Maroon">P</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Q</font> is <a href="tops_1.html#V3" target="_self">nowhere_dense</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T45" target="_self">Th45</a></i>;<br/>


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