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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="tex_3.html#V1" target="_self">dense</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>reconsider </b><font color="Maroon">C</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="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/>
<a NAME="E2:16"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">C</font> is <a href="tops_1.html#V1">dense</a>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E3:16"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X2</font>
 ;<br/>

<a NAME="E4:16"/>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X2</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font> holds <br/><font color="Olive">A</font> is <a href="tops_1.html#V1">dense</a>
 
<b>by </b><i>, <a class="ref" href="tops_3.html#T59">TOPS_3:59</a></i>;<br/>
<b>hence </b><a NAME="E5:16"/>
<font color="Maroon">X1</font> is  <a href="tex_3.html#V1" target="_self">dense</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X2</font>
 <b>by </b><i>, </i>;<br/>


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