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

<b>let </b><font color="Maroon">X</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X1</font> be   <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">X2</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">X2</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X1</font> #)
 ;<br/>

<b>thus </b><a NAME="E2:15"/>
( <font color="Maroon">X1</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font> implies <font color="Maroon">X2</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">X1</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">Y2</font> = <font color="Maroon">X2</font> as    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font> <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">A2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<a NAME="E4:15_1"/>
<font color="Maroon">A2</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, , <a class="ref" href="tsep_1.html#T11">TSEP_1:11</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1"/>
<font color="Maroon">X2</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T11">TSEP_1:11</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:15"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">X2</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">Y1</font> = <font color="Maroon">X1</font> as    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font> <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">A1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<a NAME="E6:15"/>
<font color="Maroon">A1</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, , <a class="ref" href="tsep_1.html#T11">TSEP_1:11</a></i>;<br/>
<b>hence </b><a NAME="E7:15"/>
<font color="Maroon">X1</font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T11">TSEP_1:11</a></i>;<br/>


</div>
