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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font> being  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:78"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="tex_3.html#V2" target="_self">everywhere_dense</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V2">proper</a> )
 ;<br/>

<b>assume </b><a NAME="E2:78"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="tdlat_3.html#V3">almost_discrete</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="tdlat_3.html#V3">almost_discrete</a> <a href="pre_topc.html#NM1">TopSpace</a> ;<br/>
<a NAME="E4:78"/>
<font color="Maroon">c<sub>2</sub></font> is  non <a href="struct_0.html#V3">empty</a> <a href="tex_3.html#V2" target="_self">everywhere_dense</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="tex_3.html#E1:78"><i><font color="Green">E27</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:78"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_3.html#E1:78"><i><font color="Green">E27</font></i></a></i>;<br/>


</div>
