<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:29_1_2"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> iff <font color="Maroon">S</font> <a href="frechet.html#R1" target="_self">is_convergent_to</a> <font color="Olive">x</font> )
 <b>and </b><br/><a NAME="E2:29_1_2"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> iff <font color="Maroon">S</font> <a href="frechet.html#R1" target="_self">is_convergent_to</a> <font color="Olive">x</font> )
 ;<br/>

<a NAME="E3:29_1_2"/>
for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> iff <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>

<a NAME="E1:29_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> iff <font color="Maroon">S</font> <a href="frechet.html#R1" target="_self">is_convergent_to</a> <font color="Maroon">x</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:29_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> iff <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="frechet.html#T3" target="_self">Th3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:29_1_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T8">SUBSET_1:8</a></i>;<br/>


</div>
