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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:87"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="card_4.html#V1">countable</a>
 ;<br/>

<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E2:87"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="topgen_4.html#R1" target="_self">is_a_condensation_point_of</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E4:87"/>
not <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>2</sub></font> is <a href="card_4.html#V1">countable</a>
 
<b>by </b><i><a class="txt" href="topgen_4.html#E2:87"><i><font color="Green">E48</font></i></a>, <a class="ref" href="topgen_4.html#D9" target="_self">Def9</a></i>;<br/>
<b>hence </b><a NAME="E5:87"/>
contradiction
 <b>by </b><i><a class="txt" href="topgen_4.html#E1:87"><i><font color="Green">E47</font></i></a>, <a class="ref" href="card_4.html#T48">CARD_4:48</a></i>;<br/>


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