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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> <a href="compts_1.html#NV6" title="COMPTS_1:NV.6">Hausdorff</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">N</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:87"/><i><font color="Green" title="E40">A1</font></i>: 
for <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">d</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">c</font> <a href="waybel_9.html#R3" title="WAYBEL_9:pred.3">is_a_cluster_point_of</a> <font color="Maroon" title="c2">N</font> &amp; <font color="Olive" title="b2">d</font> <a href="waybel_9.html#R3" title="WAYBEL_9:pred.3">is_a_cluster_point_of</a> <font color="Maroon" title="c2">N</font> holds <br/><font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">d</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">c</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>assume </b><a NAME="E2:87"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="waybel_9.html#R3" title="WAYBEL_9:pred.3">is_a_cluster_point_of</a> <font color="Maroon" title="c2">N</font>
 ;<br/>

<b>assume </b><a NAME="E3:87"/>
not <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Maroon" title="c2">N</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">M</font> being    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c2">N</font><b> such that </b><br/><a NAME="E5:87"/><i><font color="Green" title="E42">A3</font></i>: 
for <font color="Olive" title="b1">P</font> being   <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c4">M</font>  holds not <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Olive" title="b1">P</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#T46" title="YELLOW_6:th.46">YELLOW_6:46</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">d</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E7:87"/><i><font color="Green" title="E43">A4</font></i>: 
<font color="Maroon" title="c5">d</font> <a href="waybel_9.html#R3" title="WAYBEL_9:pred.3">is_a_cluster_point_of</a> <font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="ref" href="waybel_9.html#T30" target="_self" title="WAYBEL_9:th.30">Th30</a></i>;<br/>
<a NAME="E8:87"/><i><font color="Green" title="E44">A5</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">d</font>
 
<b>by </b><i><a class="txt" href="waybel_9.html#E5:87"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="waybel_9.html#E7:87"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="waybel_9.html#T32" target="_self" title="WAYBEL_9:th.32">Th32</a></i>;<br/>
<a NAME="E9:87"/>
<font color="Maroon" title="c5">d</font> <a href="waybel_9.html#R3" title="WAYBEL_9:pred.3">is_a_cluster_point_of</a> <font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="txt" href="waybel_9.html#E7:87"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="waybel_9.html#T31" target="_self" title="WAYBEL_9:th.31">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" title="E40">A1</font></i></a>, <a class="txt" href="waybel_9.html#E2:87"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="waybel_9.html#E8:87"><i><font color="Green" title="E44">A5</font></i></a></i>;<br/>


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