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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <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>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/>

<b>reconsider </b><font color="Maroon">B2</font> = <font color="Maroon">B</font> as   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E3:13"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">B2</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i>, <a class="ref" href="treal_1.html#T4">TREAL_1:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">I1</font> = <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<a NAME="E5:13"/><i><font color="Green">E31</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">I1</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a>, <a class="ref" href="pre_topc.html#D10">PRE_TOPC:def 10</a></i>;<br/>
<a NAME="E6:13"/><i><font color="Green">E35</font></i>: 
 <a href="topmetr.html#K5">I[01]</a>  <a href="hidden.html#R1">=</a> <a href="topmetr.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">I1</font>
 
<b>by </b><i><a class="ref" href="topmetr.html#T26">TOPMETR:26</a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a></i>;<br/>
<a NAME="E7:13"/>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><a href="topmetr.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">I1</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<b>hence </b><a NAME="E8:13"/>
<font color="Maroon">B</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i>, , <a class="ref" href="pre_topc.html#T43">PRE_TOPC:43</a></i>;<br/>


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