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<span class="kw">reconsider </span><font color="Maroon" title="c1">B</font> =  <a href="borsuk_5.html#K1" title="BORSUK_5:func.1">IRRAT</a>  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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">A</font> =  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="numbers.html#T12" title="NUMBERS:th.12">NUMBERS:12</a>, <a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">A</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">B</font> being  <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>  st <br/>( <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; <font color="Olive" title="b1">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; not <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b1">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c1">B</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; <font color="Maroon" title="c1">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; not <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c1">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  )</span><br/>

<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c1">B</font> = 
<a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_5.html#D3" title="BORSUK_5:def.3">BORSUK_5:def 3</a>, <a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>
<br/>.= 
 <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="numbers.html#T12" title="NUMBERS:th.12">NUMBERS:12</a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:91"/>
( <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; <font color="Maroon" title="c1">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; not <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c1">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_1.html#T56" target="_self" title="TOPGEN_1:th.56">Th56</a>, <a class="ref" href="topgen_1.html#T57" target="_self" title="TOPGEN_1:th.57">Th57</a>, <a class="ref" href="topgen_1.html#T58" target="_self" title="TOPGEN_1:th.58">Th58</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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