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<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ;<br/>

<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c1">p1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">p2</font>
 ;<br/>

<a NAME="E2:28"/><i><font color="Green" title="E23">A2</font></i>: 
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">p1</font> &amp; <font color="Maroon" title="c2">p2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T86" title="BORSUK_1:th.86">BORSUK_1:86</a></i>;<br/>
<b>set </b><font color="Maroon" title="c3">S</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">S</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <b>by </b><i><a class="ref" href="borsuk_1.html#T83" title="BORSUK_1:th.83">BORSUK_1:83</a>, <a class="ref" href="rcomp_1.html#T16" title="RCOMP_1:th.16">RCOMP_1:16</a></i>;<br/>
<a NAME="E4:28"/><i><font color="Green" title="E24">A3</font></i>: 
<font color="Maroon" title="c4">S</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="ref" href="borsuk_4.html#T48" target="_self" title="BORSUK_4:th.48">Th48</a></i>;<br/>
<a NAME="E5:28"/><i><font color="Green" title="E25">A4</font></i>: 
 <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E1:28"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="treal_1.html#T23" title="TREAL_1:th.23">TREAL_1:23</a></i>;<br/>
<a NAME="E6:28"/>
<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E1:28"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="borsuk_4.html#E2:28"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="topmetr.html#T31" title="TOPMETR:th.31">TOPMETR:31</a></i>;<br/>
<b>hence </b><a NAME="E7:28"/>
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> 
 <b>by </b><i><a class="txt" href="borsuk_4.html#E1:28"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="borsuk_4.html#E4:28"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="borsuk_4.html#E5:28"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="compts_1.html#T17" title="COMPTS_1:th.17">COMPTS_1:17</a>, <a class="ref" href="connsp_1.html#D3" title="CONNSP_1:def.3">CONNSP_1:def 3</a>, <a class="ref" href="rcomp_1.html#T15" title="RCOMP_1:th.15">RCOMP_1:15</a></i>;<br/>


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