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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="borsuk_5.html#K1" title="BORSUK_5:func.1">IRRAT</a>  implies <font color="Maroon" title="c1">A</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> )</span><br/>

<b>assume </b><a NAME="E1:86"/>
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="borsuk_5.html#K1" title="BORSUK_5:func.1">IRRAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">A</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a></span><br/>

<a NAME="E2:86"/><b>then </b>
<font color="Maroon" title="c1">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E66"><i><font color="Green" title="E43">Lm3</font></i></a>, <a class="ref" href="topgen_1.html#T54" target="_self" title="TOPGEN_1:th.54">Th54</a>, <a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<b>hence </b><a NAME="E3:86"/>
<font color="Maroon" title="c1">A</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>
 <b>by </b><i><a class="ref" href="tops_1.html#D4" title="TOPS_1:def.4">TOPS_1:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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