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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:50"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">S</font> <a href="frechet.html#R1">is_convergent_to</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:50"/>
 ex <font color="Olive">S1</font> being   <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">S</font> st <font color="Olive">S1</font> <a href="frechet.html#R1">is_convergent_to</a> <font color="Maroon">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">S1</font> = <font color="Maroon">S</font> as    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">S1</font>
;<br/>

<b>thus </b><a NAME="E2:50_1"/>
<font color="Maroon">S1</font> <a href="frechet.html#R1">is_convergent_to</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="frechet2.html#T1" target="_self">Th1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:50"/>
<font color="Maroon">x</font> <a href="frechet2.html#R1" target="_self">is_a_cluster_point_of</a> <font color="Maroon">S</font>
 <b>by </b><i/>;<br/>


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