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<b>reconsider </b><font color="Maroon">c<sub>1</sub></font> =  <a href="pre_topc.html#K1">{}</a> <a href="topmetr.html#K3">R^1</a>  as   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  ;<br/>
<b>assume </b><a NAME="E2:54_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K2" target="_self">Kurat14Set</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setfam_1.html#D9">SETFAM_1:def 9</a><br/>

<a NAME="E3:54_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K2" target="_self">Kurat14Set</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 
<b>by </b><i><a class="ref" href="kurato_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E4:54_1_1"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <a href="topmetr.html#K3">R^1</a>  <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K2" target="_self">Kurat14Set</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 
;<br/>
<a NAME="E5:54_1_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K3">R^1</a>  <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K2" target="_self">Kurat14Set</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 
;<br/>
<b>hence </b><a NAME="E6:54_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="borsuk_5.html#D6">BORSUK_5:def 6</a></i>;<br/>


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