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<a NAME="E1:100_1_1"/>
 <a href="borsuk_1.html#K17" target="_self">TrivExt</a> <font color="Maroon">D</font> is <a href="borsuk_1.html#V2" target="_self">DECOMPOSITION-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:100_1_1_1"/><i><font color="Green">E24</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K14" target="_self">space</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">XX</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="E2:100_1_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="borsuk_1.html#K17" target="_self">TrivExt</a> <font color="Maroon">D</font>
 ;<br/>

<b>then consider </b><font color="Maroon">W</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">XX</font><b> such that </b><br/><a NAME="E4:100_1_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K2" target="_self">proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K17" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">W</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:100_1_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K17" target="_self">TrivExt</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">W</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:100_1_1_1_1_1"/>
( <font color="Maroon">W</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> or  not <font color="Maroon">W</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:100_1_1_1_1_1_1"/>
<font color="Maroon">W</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">W'</font> = <font color="Maroon">W</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font> ;<br/><a NAME="E3:100_1_1_1_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" target="_self">Proj</a> <font color="Maroon">D</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">W'</font>
 <b>by </b><i>, <a class="ref" href="borsuk_1.html#T19" target="_self">Th19</a></i>;<br/><b>then reconsider </b><font color="Maroon">B</font> = <font color="Maroon">A</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="borsuk_1.html#T27" target="_self">Th27</a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E5:100_1_1_1_1_1_1"/>
<font color="Maroon">B</font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i><a class="ref" href="borsuk_1.html#T27" target="_self">Th27</a>, <a class="ref" href="borsuk_1.html#D1" target="_self">Def1</a>, <a class="ref" href="borsuk_1.html#T26" target="_self">Th26</a></i>;<br/><b>hence </b><a NAME="E6:100_1_1_1_1_1_1"/>
<font color="Maroon">A</font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E5:100_1_1_1"><i><font color="Green">E31</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="100_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:100_1_1_1_1_1_2"/>
not <font color="Maroon">W</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 ;<br/><div class="add"><a NAME="E2:100_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">W</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:100_1_1_1_1_1_2"/>
<font color="Maroon">A</font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:100_1_1_1"/>
<font color="Maroon">A</font> is <a href="compts_1.html#V6">compact</a>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:100_1_1"/>
 <a href="borsuk_1.html#K16" target="_self">TrivExt</a> <font color="Maroon">D</font> is   <a href="borsuk_1.html#NM2">DECOMPOSITION</a> of <font color="Maroon">XX</font>
 ;<br/>


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