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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>assume </b><a NAME="E1:86"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#K1">IRRAT</a> 
 ;<br/>

<a NAME="E2:86"/>
<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a>  <a href="numbers.html#K3">RAT</a> 
 
<b>by </b><i><a class="txt" href="topgen_1.html#E66"><i><font color="Green">Lemma45</font></i></a>, <a class="txt" href="topgen_1.html#E1:86"><i><font color="Green">E50</font></i></a>, <a class="ref" href="borsuk_5.html#T13">BORSUK_5:13</a></i>;<br/>
<a NAME="E3:86"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a>  is <a href="tops_1.html#V1">dense</a>
 
<b>by </b><i><a class="ref" href="topgen_1.html#T54" target="_self">Th54</a></i>;<br/>
<b>hence </b><a NAME="E4:86"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="tops_1.html#V2">boundary</a>
 <b>by </b><i><a class="ref" href="tops_1.html#D4">TOPS_1:def 4</a></i>;<br/>


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