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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">A</font> is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a> holds <br/>for <font color="Olive" title="b2">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>  holds not <font color="Olive" title="b2">x</font> <a href="topgen_4.html#R1" title="TOPGEN_4:pred.1">is_a_condensation_point_of</a> <font color="Olive" title="b1">A</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a> implies for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>  holds not <font color="Olive" title="b1">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> )</span><br/>



<b>assume </b><a NAME="E1:86"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>  holds not <font color="Olive" title="b1">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></span><br/>

<b>given </b><font color="Maroon" title="c3">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><b> such that </b><a NAME="E3:86"/><i><font color="Green" title="E48">A2</font></i>: 
<font color="Maroon" title="c3">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>consider </b><font color="Maroon" title="c4">N</font> being    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c3">x</font>;<br/>
<a NAME="E5:86"/>
not <font color="Maroon" title="c4">N</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">A</font> is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>
 
<b>by </b><i><a class="txt" href="#E3:86"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="topgen_4.html#D9" target="_self" title="TOPGEN_4:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E6:86"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:86"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="card_3.html#T129" title="CARD_3:th.129">CARD_3:129</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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