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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:74"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_1.html#K13" target="_self">TrivDecomp</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="connsp_2.html#M2">a_neighborhood</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>take </b>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E2:74"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>thus </b><a NAME="E3:74"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="connsp_2.html#D2">CONNSP_2:def 2</a></i>;<br/>

<b>thus </b><a NAME="E4:74"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="tops_1.html#T44">TOPS_1:44</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E5:74"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_1.html#K13" target="_self">TrivDecomp</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E6:74"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:74"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E5:74"><i><font color="Green">E56</font></i></a>, <a class="ref" href="borsuk_1.html#T68" target="_self">Th68</a></i>;<br/>
<a NAME="E9:74"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E6:74"><i><font color="Green">E57</font></i></a>, <a class="txt" href="borsuk_1.html#E8:74"><i><font color="Green">E58</font></i></a>, <a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/>
<b>hence </b><a NAME="E10:74"/>
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E8:74"><i><font color="Green">E58</font></i></a>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>


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