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

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

<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="compts_1.html#NR2" target="_self">is_T2</a> 
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="compts_1.html#V2" target="_self">compact</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="compts_1.html#D5" target="_self">COMPTS_1:def 5</a><br/><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><b>that </b><br/><a NAME="E3:18"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E4:18"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>and </b><br/><a NAME="E5:18"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> 
 ;<br/>

<a NAME="E6:18"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="compts_1.html#V6" target="_self">compact</a>
 
<b>by </b><i><a class="txt" href="compts_1.html#E2:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="compts_1.html#E4:18"><i><font color="Green">E18</font></i></a>, <a class="ref" href="compts_1.html#T17" target="_self">Th17</a></i>;<br/>
<b>hence </b><a NAME="E7:18"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="compts_1.html#E1:18"><i><font color="Green">E15</font></i></a>, <a class="txt" href="compts_1.html#E3:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="compts_1.html#E5:18"><i><font color="Green">E19</font></i></a>, <a class="ref" href="compts_1.html#T15" target="_self">Th15</a></i>;<br/>


</div>
