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<b>let </b><font color="Maroon">c<sub>1</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>2</sub></font>, <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><a NAME="E1:51"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#K2">RAT</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a>  = 
<a href="numbers.html#K1">REAL</a>  <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="borsuk_5.html#T83">BORSUK_5:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_5.html#NK1" target="_self">].-infty,</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="borsuk_5.html#K3">IRRAT</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="borsuk_5.html#NK3" target="_self">[.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isomichi.html#E1:51"><i><font color="Green">E21</font></i></a>, <a class="ref" href="borsuk_5.html#T85">BORSUK_5:85</a></i>
;<br/>
<b>then </b> <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K3">R^1</a> 
<b>by </b><i><a class="ref" href="isomichi.html#T30" target="_self">Th30</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <a href="topmetr.html#K3">R^1</a> 
<b>by </b><i><a class="ref" href="pre_topc.html#D3">PRE_TOPC:def 3</a></i>
;<br/>
<a NAME="E4:51"/><b>then </b>
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <a href="topmetr.html#K3">R^1</a> 
 
<b>by </b><i><a class="ref" href="tops_1.html#T8">TOPS_1:8</a></i>;<br/>
<b>hence </b><a NAME="E5:51"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="tops_1.html#D1">TOPS_1:def 1</a></i>;<br/>


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