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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ;<br/><b>let </b><font color="Maroon" title="c3">b</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:84"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,<font color="Maroon" title="c3">b</font></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green" title="E57">A2</font></i>: 
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><font color="Maroon" title="c3">b</font>,<a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a> </span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 ;<br/>

<a NAME="E3:84"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,<font color="Maroon" title="c3">b</font></span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E1:84"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="borsuk_5.html#T77" target="_self" title="BORSUK_5:th.77">Th77</a></i>;<br/>
<a NAME="E4:84"/><b>then </b><i><font color="Green" title="E58">A3</font></i>: 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:84"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="xxreal_1.html#T91" title="XXREAL_1:th.91">XXREAL_1:91</a></i>;<br/>
<a NAME="E5:84"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_2.html#K1" title="RCOMP_2:func.1">[.</a><span class="default"><font color="Maroon" title="c3">b</font>,<a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a> </span><a href="rcomp_2.html#K1" title="RCOMP_2:func.1">.[</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:84"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="borsuk_5.html#T75" target="_self" title="BORSUK_5:th.75">Th75</a></i>;<br/>
<a NAME="E6:84"/><b>then </b>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">B</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E1:84"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="xxreal_1.html#T94" title="XXREAL_1:th.94">XXREAL_1:94</a></i>;<br/>
<b>hence </b><a NAME="E7:84"/>
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> 
 <b>by </b><i><a class="txt" href="borsuk_5.html#E4:84"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="connsp_1.html#D1" title="CONNSP_1:def.1">CONNSP_1:def 1</a></i>;<br/>


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