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<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:46_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_3.html#V4" target="_self">nowhere_dense</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:46_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:46_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is <a href="tops_1.html#V3">nowhere_dense</a>
 <b>by </b><i><a class="txt" href="tex_3.html#E1:46_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="tex_3.html#D4" target="_self">Def4</a></i>;<br/><b>hence </b><a NAME="E3:46_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tops_1.html#V2">boundary</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T92">TOPS_1:92</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:46_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_3.html#V3" target="_self">boundary</a>
 <b>by </b><i><a class="ref" href="tex_3.html#D3" target="_self">Def3</a></i>;<br/>


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