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<a NAME="E1:20_1_1"/>
 <a href="numbers.html#K1">REAL</a>  <a href="tarski.html#R1">c=</a> 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="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">P</font> =  <a href="numbers.html#K1">REAL</a>  as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  ;<br/>
<b>take </b>
<font color="Maroon">P</font>
;<br/>

<b>thus </b><a NAME="E3:20_1_1"/>
not <font color="Maroon">P</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K3">R^1</a> , <font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K3">R^1</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="topalg_2.html#D3" target="_self">TOPALG_2:def 3</a><br/>

<b>thus </b><a NAME="E4:20_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> implies <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> )
 ;<br/>


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