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<b>take </b>
 <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> 
;<br/>

<b>set </b><font color="Maroon" title="c1">B</font> = <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>;<br/>
<b>set </b><font color="Maroon" title="c2">C</font> =  <a href="borsuk_5.html#K2" title="BORSUK_5:func.2">RAT</a> 2,4;<br/>
<b>set </b><font color="Maroon" title="c3">A</font> = <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="borsuk_5.html#K2" title="BORSUK_5:func.2">RAT</a> 2,4</span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">A</font> = <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="borsuk_5.html#K2" title="BORSUK_5:func.2">RAT</a> 2,4</span>)</span>, <font color="Maroon" title="c5">B</font> = <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>, <font color="Maroon" title="c6">C</font> =  <a href="borsuk_5.html#K2" title="BORSUK_5:func.2">RAT</a> 2,4 as   <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>  <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<a NAME="E2:74_2_1"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 
<b>by </b><i><a class="ref" href="isomichi.html#T37" target="_self" title="ISOMICHI:th.37">Th37</a></i>;<br/>
<a NAME="E3:74_2_1"/><b>then </b><i><font color="Green" title="E38">A2</font></i>: 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T77" title="BORSUK_5:th.77">BORSUK_5:77</a></i>;<br/>
<a NAME="E4:74_2_1"/><i><font color="Green" title="E39">A3</font></i>: 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T77" title="BORSUK_5:th.77">BORSUK_5:77</a></i>;<br/>
<a NAME="E5:74_2_1"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default">2,4</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T54" title="BORSUK_5:th.54">BORSUK_5:54</a></i>;<br/>
<a NAME="E6:74_2_1"/><b>then </b>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default">2,4</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<b>by </b><i><a class="txt" href="isomichi.html#E4:74_2_1"><i><font color="Green" title="E39">A3</font></i></a>, <a class="ref" href="pre_topc.html#T50" title="PRE_TOPC:th.50">PRE_TOPC:50</a></i>;<br/>
<a NAME="E7:74_2_1"/><b>then </b><i><font color="Green" title="E40">A4</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">2,4</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 
<b>by </b><i><a class="ref" href="isomichi.html#T44" target="_self" title="ISOMICHI:th.44">Th44</a></i>;<br/>
<a NAME="E8:74_2_1"/>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">2,4</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/>
<a NAME="E9:74_2_1"/><b>then </b>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isomichi.html#E7:74_2_1"><i><font color="Green" title="E40">A4</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E10:74_2_1"/><b>then </b><i><font color="Green" title="E41">A5</font></i>: 
not  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isomichi.html#E3:74_2_1"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="borsuk_5.html#T16" title="BORSUK_5:th.16">BORSUK_5:16</a></i>;<br/>
<a NAME="E11:74_2_1"/><i><font color="Green" title="E42">A6</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isomichi.html#E3:74_2_1"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="borsuk_5.html#T16" title="BORSUK_5:th.16">BORSUK_5:16</a></i>;<br/>
<a NAME="E12:74_2_1"/>
( not 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> ,1</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> &amp; not 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default">2,4</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> )
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T17" title="BORSUK_5:th.17">BORSUK_5:17</a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/>
<a NAME="E13:74_2_1"/><b>then </b>
not  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isomichi.html#E11:74_2_1"><i><font color="Green" title="E42">A6</font></i></a>, <a class="txt" href="isomichi.html#E7:74_2_1"><i><font color="Green" title="E40">A4</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E14:74_2_1"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c4">A</font></span>)</span>, <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="isomichi.html#NR1" title="ISOMICHI:NR.1">are_c=-incomparable</a> 
 
<b>by </b><i><a class="txt" href="isomichi.html#E10:74_2_1"><i><font color="Green" title="E41">A5</font></i></a>, <a class="ref" href="xboole_0.html#D9" title="XBOOLE_0:def.9">XBOOLE_0:def 9</a></i>;<br/>
<a NAME="E15:74_2_1"/><b>then </b>
<font color="Maroon" title="c4">A</font> is <a href="isomichi.html#V5" title="ISOMICHI:attr.5">3rd_class</a>
 
<b>by </b><i><a class="ref" href="isomichi.html#D8" target="_self" title="ISOMICHI:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E16:74_2_1"/>
(  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  is <a href="isomichi.html#V8" title="ISOMICHI:attr.8">with_3rd_class_subsets</a> &amp; not  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp;  <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> )
 <b>by </b><i><a class="ref" href="isomichi.html#D11" target="_self" title="ISOMICHI:def.11">Def11</a></i>;<br/>


</div>
