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<b>let </b><font color="Maroon">A</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">a</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="E1:48"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#NK1" target="_self">].-infty,</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:48"/><b>then </b>
<font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#NK4" target="_self">].</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T98">BORSUK_5:98</a></i>;<br/>
<a NAME="E3:48"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#NK3" target="_self">[.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T75">BORSUK_5:75</a></i>;<br/>
<a NAME="E4:48"/><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">A</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="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T99">BORSUK_5:99</a></i>;<br/>
<b>hence </b><a NAME="E5:48"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#NK2" target="_self">].-infty,</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="tops_1.html#D1">TOPS_1:def 1</a></i>;<br/>


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