<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></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">E69</font></i>: 
<font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font></span><a href="borsuk_5.html#NK2" target="_self">.[</a></span>
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></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">c<sub>1</sub></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">c<sub>3</sub></font></span><a href="borsuk_5.html#NK1" target="_self">.]</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E1:84"><i><font color="Green">E69</font></i></a>, <a class="ref" href="borsuk_5.html#T77" target="_self">Th77</a></i>;<br/>
<a NAME="E4:84"/><b>then </b><i><font color="Green">E71</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:84"><i><font color="Green">E70</font></i></a>, <a class="ref" href="borsuk_5.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E5:84"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:84"><i><font color="Green">E70</font></i></a>, <a class="ref" href="borsuk_5.html#T75" target="_self">Th75</a></i>;<br/>
<a NAME="E6:84"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E1:84"><i><font color="Green">E69</font></i></a>, <a class="ref" href="borsuk_5.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E7:84"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="connsp_1.html#R1">are_separated</a> 
 <b>by </b><i><a class="txt" href="borsuk_5.html#E4:84"><i><font color="Green">E71</font></i></a>, <a class="ref" href="connsp_1.html#D1">CONNSP_1:def 1</a></i>;<br/>


</div>
