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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>assume </b><a NAME="E1:87"/><i><font color="Green" title="E48">A1</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a>
 ;<br/>

<b>assume </b><a NAME="E2:87"/>
<font color="Maroon" title="c2">A</font> <a href="topgen_4.html#K4" title="TOPGEN_4:func.4">^0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:87"/><i><font color="Green" title="E49">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="topgen_4.html#K4" title="TOPGEN_4:func.4">^0</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">x'</font> = <font color="Maroon" title="c3">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> <b>by </b><i><a class="txt" href="topgen_4.html#E4:87"><i><font color="Green" title="E49">A2</font></i></a></i>;<br/>
<a NAME="E6:87"/>
<font color="Maroon" title="c4">x'</font> <a href="topgen_4.html#R1" title="TOPGEN_4:pred.1">is_a_condensation_point_of</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E4:87"><i><font color="Green" title="E49">A2</font></i></a>, <a class="ref" href="topgen_4.html#D10" target="_self" title="TOPGEN_4:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E7:87"/>
contradiction
 <b>by </b><i><a class="txt" href="topgen_4.html#E1:87"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="topgen_4.html#T58" target="_self" title="TOPGEN_4:th.58">Th58</a></i>;<br/>


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