<?xml version="1.0"?>
<div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c3">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#T17" title="TOPMETR:th.17">TOPMETR:17</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">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#T17" title="TOPMETR:th.17">TOPMETR:17</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">A</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c4">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="c4">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="c3">B</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">A</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; <font color="Maroon" title="c3">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp;  not <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  )</span><br/>

<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">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#D1" title="BORSUK_5:def.1">BORSUK_5:def 1</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="E4:88"/>
( <font color="Maroon" title="c4">A</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp; <font color="Maroon" title="c3">B</font> is  <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>  &amp;  not <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">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#T53" target="_self" title="TOPGEN_1:th.53">Th56</a>, <a class="ref" href="topgen_1.html#T54" target="_self" title="TOPGEN_1:th.54">Th57</a>, <a class="ref" href="topgen_1.html#T55" target="_self" title="TOPGEN_1:th.55">Th58</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
