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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:86_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V3">nowhere_dense</a>
 <b>by </b><i><a class="ref" href="tex_1.html#D7">TEX_1:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:86_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:86_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>and </b><br/><a NAME="E6:86_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="tops_1.html#V2">boundary</a>
 <b>by </b><i><a class="txt" href="tex_3.html#E2:86_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="tops_3.html#T27">TOPS_3:27</a></i>;<br/>
<a NAME="E7:86_1_1"/>
not <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E4:86_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:86_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T10">TSEP_1:10</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<a NAME="E10:86_1_1"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="tops_1.html#V2">boundary</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E6:86_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="tex_3.html#E9:86_1_1"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E11:86_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E5:86_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="tex_3.html#E9:86_1_1"><i><font color="Green">E32</font></i></a></i>;<br/>
<b>hence </b><a NAME="E12:86_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="tex_3.html#V3" target="_self">boundary</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="borsuk_1.html#V1">closed</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V1">strict</a> &amp; not <font color="Maroon">c<sub>4</sub></font> is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i><a class="txt" href="tex_3.html#E10:86_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="tex_3.html#D3" target="_self">Def3</a>, <a class="ref" href="borsuk_1.html#D14">BORSUK_1:def 14</a></i>;<br/>


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