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<span class="kw">let </span><font color="Maroon" title="c2">X0</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">X0</font> is  <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a>  implies <font color="Maroon" title="c2">X0</font> is  <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:41_2_1"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c2">X0</font> is  <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">X0</font> is  <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tsep_1.html#D1" title="TSEP_1:def.1">TSEP_1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> or <font color="Maroon" title="c3">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:41_2_1"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> </span><br/>

<a NAME="E3:41_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">A</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41_2_1"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="borsuk_1.html#D11" title="BORSUK_1:def.11">BORSUK_1:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:41_2_1"/>
<font color="Maroon" title="c3">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#T22" target="_self" title="TDLAT_3:th.22">Th24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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