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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  <a href="pre_topc.html#V1">strict</a> <a href="pre_topc.html#NM1">TopSpace</a><b> such that </b><br/><a NAME="E2:83"/><i><font color="Green">E40</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="yellow_9.html#E58"><i><font color="Green">Lemma37</font></i></a></i>;<br/>
<a NAME="E3:83"/>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="yellow_9.html#E2:83"><i><font color="Green">E40</font></i></a>, <a class="ref" href="cantor_1.html#D5">CANTOR_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="yellow_9.html#M2" target="_self">TopExtension</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="yellow_9.html#E2:83"><i><font color="Green">E40</font></i></a>, <a class="ref" href="yellow_9.html#D5" target="_self">Def5</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E5:83"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V1">strict</a> &amp; the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="yellow_9.html#E2:83"><i><font color="Green">E40</font></i></a></i>;<br/>


</div>
