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<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> , <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:84"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_5.html#NK2" target="_self">].-infty,</a><span class="default"><font color="Maroon">b</font></span><a href="borsuk_5.html#NK2" target="_self">.[</a></span>
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_5.html#NK4" target="_self">].</a><span class="default"><font color="Maroon">b</font></span><a href="borsuk_5.html#NK4" target="_self">,+infty.[</a></span>
 ;<br/>

<a NAME="E3:84"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_5.html#NK1" target="_self">].-infty,</a><span class="default"><font color="Maroon">b</font></span><a href="borsuk_5.html#NK1" target="_self">.]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T18" target="_self">Th18</a>, <a class="ref" href="borsuk_5.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E4:84"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T19" target="_self">Th19</a>, </i>;<br/>
<a NAME="E5:84"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">b</font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T19" target="_self">Th19</a>, <a class="ref" href="borsuk_5.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E6:84"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T18" target="_self">Th18</a>, </i>;<br/>
<b>hence </b><a NAME="E7:84"/>
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="connsp_1.html#R1">are_separated</a> 
 <b>by </b><i>, <a class="ref" href="connsp_1.html#D1">CONNSP_1:def 1</a></i>;<br/>


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