<?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="compts_1.html#V2">compact</a> <a href="compts_1.html#V3">Hausdorff</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:87"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="waybel_9.html#R3" target="_self">is_a_cluster_point_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="waybel_9.html#R3" target="_self">is_a_cluster_point_of</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E2:87"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="waybel_9.html#R3" target="_self">is_a_cluster_point_of</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:87"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11">Lim</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E5:87"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">c<sub>4</sub></font> holds not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11">Lim</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="yellow_6.html#T46">YELLOW_6:46</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:87"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="waybel_9.html#R3" target="_self">is_a_cluster_point_of</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="waybel_9.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E8:87"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_9.html#E5:87"><i><font color="Green">E42</font></i></a>, <a class="txt" href="waybel_9.html#E7:87"><i><font color="Green">E43</font></i></a>, <a class="ref" href="waybel_9.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E9:87"/>
<font color="Maroon">c<sub>5</sub></font> <a href="waybel_9.html#R3" target="_self">is_a_cluster_point_of</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_9.html#E7:87"><i><font color="Green">E43</font></i></a>, <a class="ref" href="waybel_9.html#T31" target="_self">Th31</a></i>;<br/>
<b>hence </b><a NAME="E10:87"/>
contradiction
 <b>by </b><i><a class="txt" href="waybel_9.html#E1:87"><i><font color="Green">E40</font></i></a>, <a class="txt" href="waybel_9.html#E2:87"><i><font color="Green">E41</font></i></a>, <a class="txt" href="waybel_9.html#E8:87"><i><font color="Green">E44</font></i></a></i>;<br/>


</div>
