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<b>consider </b><font color="Maroon" title="c2">A</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E2:86_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="tops_1.html#V3" title="TOPS_1:attr.3">nowhere_dense</a>
 <b>by </b><i><a class="ref" href="tex_1.html#D7" title="TEX_1:def.7">TEX_1:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:86_1_1"/><i><font color="Green" title="E29">A2</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">C</font>
 <b>and </b><br/><a NAME="E5:86_1_1"/><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c3">C</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E6:86_1_1"/><i><font color="Green" title="E31">A4</font></i>: 
<font color="Maroon" title="c3">C</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>
 <b>by </b><i><a class="txt" href="tex_3.html#E2:86_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="tops_3.html#T27" title="TOPS_3:th.27">TOPS_3:27</a></i>;<br/>
<a NAME="E7:86_1_1"/>
not <font color="Maroon" title="c3">C</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E4:86_1_1"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">X0</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E9:86_1_1"/><i><font color="Green" title="E32">A5</font></i>: 
<font color="Maroon" title="c3">C</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="c4">X0</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T10" title="TSEP_1:th.10">TSEP_1:10</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">X0</font>
;<br/>

<a NAME="E10:86_1_1"/><i><font color="Green" title="E33">A6</font></i>: 
for <font color="Olive" title="b1">C</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">C</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="c4">X0</font> holds <br/><font color="Olive" title="b1">C</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E6:86_1_1"><i><font color="Green" title="E31">A4</font></i></a>, <a class="txt" href="tex_3.html#E9:86_1_1"><i><font color="Green" title="E32">A5</font></i></a></i>;<br/>
<a NAME="E11:86_1_1"/>
for <font color="Olive" title="b1">C</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">C</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="c4">X0</font> holds <br/><font color="Olive" title="b1">C</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E5:86_1_1"><i><font color="Green" title="E30">A3</font></i></a>, <a class="txt" href="tex_3.html#E9:86_1_1"><i><font color="Green" title="E32">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E12:86_1_1"/>
( <font color="Maroon" title="c4">X0</font> is <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a> &amp; <font color="Maroon" title="c4">X0</font> is <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> &amp; <font color="Maroon" title="c4">X0</font> is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> &amp; not <font color="Maroon" title="c4">X0</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 <b>by </b><i><a class="txt" href="tex_3.html#E10:86_1_1"><i><font color="Green" title="E33">A6</font></i></a>, <a class="ref" href="tex_3.html#D3" target="_self" title="TEX_3:def.3">Def3</a>, <a class="ref" href="borsuk_1.html#D14" title="BORSUK_1:def.14">BORSUK_1:def 14</a></i>;<br/>


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