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

<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">S2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">T1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">T2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">R</font> be    <a href="yellow_9.html#M3">Refinement</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:60"/><i><font color="Green">E34</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>
 <b>and </b><br/><a NAME="E2:60"/><i><font color="Green">E35</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font>
 ;<br/>

<b>set </b><font color="Maroon">Y</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U1</font>,<font color="Olive">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U2</font>,<font color="Olive">V2</font></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> where <font color="Olive">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">V1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Olive">V2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V2</font> is <a href="pre_topc.html#V3">open</a> ) </span>}</span> ;<br/>
<a NAME="E3:60"/><i><font color="Green">E43</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>;<br/>
<a NAME="E4:60"/><i><font color="Green">E46</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">BST</font> =  <a href="setfam_1.html#K3">INTERSECTION</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span> as    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">R</font> <b>by </b><i>, , , <a class="ref" href="yellow_9.html#T60">YELLOW_9:60</a></i>;<br/>
<a NAME="E6:60"/><i><font color="Green">E47</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="setfam_1.html#K5">union</a> <font color="Olive">A</font></span>)</span> where <font color="Olive">A</font> is   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span> : <font color="Olive">A</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">X1</font>,<font color="Olive">Y1</font></span><a href="borsuk_1.html#K6">:]</a></span> where <font color="Olive">X1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">Y1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font> : ( <font color="Olive">X1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S1</font> &amp; <font color="Olive">Y1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> ) </span>}</span>  </span>}</span> 
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>;<br/>
<a NAME="E7:60"/><i><font color="Green">E75</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="setfam_1.html#K5">union</a> <font color="Olive">A</font></span>)</span> where <font color="Olive">A</font> is   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span> : <font color="Olive">A</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">X1</font>,<font color="Olive">Y1</font></span><a href="borsuk_1.html#K6">:]</a></span> where <font color="Olive">X1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">Y1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">X1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S2</font> &amp; <font color="Olive">Y1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> ) </span>}</span>  </span>}</span> 
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>;<br/>
<i><font color="Green">E77</font></i>: the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> = 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span>
<b>by </b><i><a class="ref" href="yellow_9.html#D6">YELLOW_9:def 6</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, <a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, </i>
;<br/>
<a NAME="E9:60"/><i><font color="Green">E80</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U1</font>,<font color="Olive">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U2</font>,<font color="Olive">V2</font></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> where <font color="Olive">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">V1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Olive">V2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V2</font> is <a href="pre_topc.html#V3">open</a> ) </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:60_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U1</font>,<font color="Olive">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U2</font>,<font color="Olive">V2</font></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> where <font color="Olive">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">V1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Olive">V2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V2</font> is <a href="pre_topc.html#V3">open</a> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">U1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Maroon">U2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Maroon">V1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Maroon">V2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font><b> such that </b><br/><a NAME="E3:60_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U1</font>,<font color="Maroon">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U2</font>,<font color="Maroon">V2</font></span><a href="borsuk_1.html#K6">:]</a></span>
 <b>and </b><br/><a NAME="E4:60_2"/><i><font color="Green">E82</font></i>: 
( <font color="Maroon">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">V2</font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>
<a NAME="E5:60_2"/>
( <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U1</font>,<font color="Maroon">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> is <a href="pre_topc.html#V3">open</a> &amp; <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U2</font>,<font color="Maroon">V2</font></span><a href="borsuk_1.html#K6">:]</a></span> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="txt" href="yellow12.html#E2:60"><i><font color="Green">E35</font></i></a>, <a class="ref" href="borsuk_1.html#T46">BORSUK_1:46</a></i>;<br/>
<a NAME="E6:60_2"/><b>then </b>
( <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U1</font>,<font color="Maroon">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span> &amp; <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U2</font>,<font color="Maroon">V2</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E7:60_2"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BST</font>
 
<b>by </b><i><a class="txt" href="yellow12.html#E1:60"><i><font color="Green">E34</font></i></a>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E8:60_2"/>
<font color="Maroon">BST</font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D2">CANTOR_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E9:60_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">R</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E10:60"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U1</font>,<font color="Olive">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U2</font>,<font color="Olive">V2</font></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> where <font color="Olive">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">V1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Olive">V2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V2</font> is <a href="pre_topc.html#V3">open</a> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:60_3"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U1</font>,<font color="Olive">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U2</font>,<font color="Olive">V2</font></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> where <font color="Olive">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">V1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Olive">V2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V2</font> is <a href="pre_topc.html#V3">open</a> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">U1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Maroon">U2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Maroon">V1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Maroon">V2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font><b> such that </b><br/><a NAME="E3:60_3"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U1</font>,<font color="Maroon">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U2</font>,<font color="Maroon">V2</font></span><a href="borsuk_1.html#K6">:]</a></span>
 <b>and </b><br/><a NAME="E4:60_3"/>
( <font color="Maroon">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">V2</font> is <a href="pre_topc.html#V3">open</a> )
 ;<br/>
<a NAME="E5:60_3"/>
<span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U1</font>,<font color="Maroon">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">U2</font>,<font color="Maroon">V2</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<b>hence </b><a NAME="E6:60_3"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>
 <b>by </b><i>, , , <a class="txt" href="yellow12.html#E1:60"><i><font color="Green">E34</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">C1</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U1</font>,<font color="Olive">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U2</font>,<font color="Olive">V2</font></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> where <font color="Olive">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">V1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Olive">V2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V2</font> is <a href="pre_topc.html#V3">open</a> ) </span>}</span>  as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">R</font> ;<br/>
<b>reconsider </b><font color="Maroon">C1</font> = <font color="Maroon">C1</font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">R</font> ;<br/>
<a NAME="E13:60"/>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>  st <font color="Olive">A</font> is <a href="pre_topc.html#V3">open</a> holds <br/>for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">R</font>  st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> holds <br/> ex <font color="Olive">a</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> &amp; <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>;<br/>

<b>assume </b><a NAME="E1:60_4"/><i><font color="Green">E121</font></i>: 
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">R</font>;<br/>

<b>assume </b><a NAME="E2:60_4"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon">X</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E4:60_4"/><i><font color="Green">E122</font></i>: 
( <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BST</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="txt" href="yellow12.html#E1:60"><i><font color="Green">E34</font></i></a>, <a class="ref" href="yellow_9.html#T31">YELLOW_9:31</a></i>;<br/>
<b>consider </b><font color="Maroon">X1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">X2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:60_4"/><i><font color="Green">E123</font></i>: 
<font color="Maroon">X1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>and </b><br/><a NAME="E7:60_4"/><i><font color="Green">E124</font></i>: 
<font color="Maroon">X2</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>and </b><br/><a NAME="E8:60_4"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X1</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X2</font>
 <b>by </b><i><a class="txt" href="yellow12.html#E2:60"><i><font color="Green">E35</font></i></a>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">F1</font> being   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span><b> such that </b><br/><a NAME="E10:60_4"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">X1</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K5">union</a> <font color="Maroon">F1</font>
 <b>and </b><br/><a NAME="E11:60_4"/><i><font color="Green">E139</font></i>: 
<font color="Maroon">F1</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">K1</font>,<font color="Olive">L1</font></span><a href="borsuk_1.html#K6">:]</a></span> where <font color="Olive">K1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">L1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font> : ( <font color="Olive">K1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S1</font> &amp; <font color="Olive">L1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="yellow12.html#E1"><i><font color="Green">Lemma30</font></i></a>, </i>;<br/>
<b>consider </b><font color="Maroon">F2</font> being   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span><b> such that </b><br/><a NAME="E13:60_4"/><i><font color="Green">E142</font></i>: 
<font color="Maroon">X2</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K5">union</a> <font color="Maroon">F2</font>
 <b>and </b><br/><a NAME="E14:60_4"/><i><font color="Green">E143</font></i>: 
<font color="Maroon">F2</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">K2</font>,<font color="Olive">L2</font></span><a href="borsuk_1.html#K6">:]</a></span> where <font color="Olive">K2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">L2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">K2</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S2</font> &amp; <font color="Olive">L2</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> ) </span>}</span> 
 <b>by </b><i>, </i>;<br/>
<a NAME="E15:60_4"/><i><font color="Green">E145</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X2</font> )
 
<b>by </b><i><a class="txt" href="yellow12.html#E2:60"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">G1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E17:60_4"/><i><font color="Green">E147</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G1</font> &amp; <font color="Maroon">G1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F1</font> )
 <b>by </b><i><a class="ref" href="yellow12.html#T2" target="_self">Th2</a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">G2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E19:60_4"/><i><font color="Green">E149</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">G2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F2</font> )
 <b>by </b><i>, <a class="txt" href="yellow12.html#E3:60"><i><font color="Green">E43</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E20:60_4"/>
<font color="Maroon">G1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">K1</font>,<font color="Olive">L1</font></span><a href="borsuk_1.html#K6">:]</a></span> where <font color="Olive">K1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">L1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font> : ( <font color="Olive">K1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S1</font> &amp; <font color="Olive">L1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="yellow12.html#T4" target="_self">Th4</a>, <a class="ref" href="yellow12.html#T5" target="_self">Th5</a></i>;<br/>
<b>then consider </b><font color="Maroon">K1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Maroon">L1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font><b> such that </b><br/><a NAME="E22:60_4"/><i><font color="Green">E150</font></i>: 
<font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K1</font>,<font color="Maroon">L1</font></span><a href="borsuk_1.html#K6">:]</a></span>
 <b>and </b><br/><a NAME="E23:60_4"/><i><font color="Green">E151</font></i>: 
( <font color="Maroon">K1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S1</font> &amp; <font color="Maroon">L1</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> )
 ;<br/>
<a NAME="E24:60_4"/>
<font color="Maroon">G2</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">K2</font>,<font color="Olive">L2</font></span><a href="borsuk_1.html#K6">:]</a></span> where <font color="Olive">K2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">L2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">K2</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S2</font> &amp; <font color="Olive">L2</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> ) </span>}</span> 
 
<b>by </b><i>, <a class="ref" href="yellow12.html#T7" target="_self">Th7</a></i>;<br/>
<b>then consider </b><font color="Maroon">K2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Maroon">L2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font><b> such that </b><br/><a NAME="E26:60_4"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">G2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K2</font>,<font color="Maroon">L2</font></span><a href="borsuk_1.html#K6">:]</a></span>
 <b>and </b><br/><a NAME="E27:60_4"/><i><font color="Green">E153</font></i>: 
( <font color="Maroon">K2</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S2</font> &amp; <font color="Maroon">L2</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> )
 ;<br/>
<a NAME="E28:60_4"/>
<span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K1</font>,<font color="Maroon">L1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K2</font>,<font color="Maroon">L2</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">a</font> = <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K1</font>,<font color="Maroon">L1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K2</font>,<font color="Maroon">L2</font></span><a href="borsuk_1.html#K6">:]</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font> <b>by </b><i>, , </i>;<br/>
<b>take </b>
<font color="Maroon">a</font>
;<br/>

<a NAME="E30:60_4"/>
( <font color="Maroon">K1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">K2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">L1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">L2</font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="txt" href="yellow12.html#E6:60"><i><font color="Green">E47</font></i></a>, , <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<b>hence </b><a NAME="E31:60_4"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font>
 ;<br/>

<b>thus </b><a NAME="E32:60_4"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow12.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow12.html#T7" target="_self">Th7</a>, <a class="txt" href="yellow12.html#E4:60"><i><font color="Green">E46</font></i></a>, <a class="ref" href="yellow12.html#T8" target="_self">Th8</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>

<a NAME="E33:60_4"/>
( <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K1</font>,<font color="Maroon">L1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X1</font> &amp; <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">K2</font>,<font color="Maroon">L2</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X2</font> )
 
<b>by </b><i><a class="ref" href="yellow12.html#T2" target="_self">Th2</a>, , <a class="ref" href="yellow12.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow12.html#T7" target="_self">Th7</a>, <a class="txt" href="yellow12.html#E4:60"><i><font color="Green">E46</font></i></a>, <a class="ref" href="yellow12.html#T8" target="_self">Th8</a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E34:60_4"/><b>then </b>
<font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T27">XBOOLE_1:27</a></i>;<br/>
<b>hence </b><a NAME="E35:60_4"/>
<font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="txt" href="yellow12.html#E2:60"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E14:60"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U1</font>,<font color="Olive">V1</font></span><a href="borsuk_1.html#K6">:]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p3"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Olive">U2</font>,<font color="Olive">V2</font></span><a href="borsuk_1.html#K6">:]</a></span></span>)</span> where <font color="Olive">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S1</font>, <font color="Olive">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S2</font>, <font color="Olive">V1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T1</font>, <font color="Olive">V2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T2</font> : ( <font color="Olive">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V2</font> is <a href="pre_topc.html#V3">open</a> ) </span>}</span>  is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">R</font>
 <b>by </b><i>, <a class="ref" href="yellow_9.html#T32">YELLOW_9:32</a></i>;<br/>


</div>
