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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>assume </b><a NAME="E1:63"/>
( <font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font> as  <a href="pre_topc.html#V3">open</a> <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  ;<br/>
<a NAME="E3:63"/>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <a href="topmetr.html#K3">R^1</a>  )
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E4:63"/>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a>  )
 <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>


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