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

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="borsuk_1.html#K13" target="_self">TrivDecomp</a> <font color="Maroon">c<sub>1</sub></font> as    <a href="borsuk_1.html#M1" target="_self">u.s.c._decomposition</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="borsuk_1.html#T82" target="_self">Th82</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_1.html#D15" target="_self">BORSUK_1:def 15</a><br/>

<b>assume </b><a NAME="E2:98_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:98_1_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E4:98_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i><a class="ref" href="borsuk_1.html#T41" target="_self">Th41</a></i>;<br/>


</div>
