<?xml version="1.0"?>
<div class="add">

<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  <a href="tex_3.html#V2" target="_self">everywhere_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    <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="E2:25"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">C</font> is <a href="tops_3.html#V1">everywhere_dense</a>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E3:25"/>
<font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X2</font>
 ;<br/>

<a NAME="E4:25"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T4">TSEP_1:4</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</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">X2</font> holds <br/><font color="Olive">A</font> is <a href="tops_3.html#V1">everywhere_dense</a>
 
<b>by </b><i>, <a class="ref" href="tops_3.html#T38">TOPS_3:38</a></i>;<br/>
<b>hence </b><a NAME="E6:25"/>
<font color="Maroon">X2</font> is <a href="tex_3.html#V2" target="_self">everywhere_dense</a>
 <b>by </b><i/>;<br/>


</div>
