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

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D3" target="_self" title="BORSUK_2:def.3">BORSUK_2:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a> </span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_1_1_1"/>
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> or <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_1_1"><b>suppose </b></a><a NAME="E1:49_1_1_1_1"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a> </span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c3">B</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <b>by </b><i><a class="ref" href="borsuk_1.html#T83" title="BORSUK_1:th.83">BORSUK_1:83</a>, <a class="ref" href="rcomp_1.html#T15" title="RCOMP_1:th.15">RCOMP_1:15</a>, <a class="ref" href="rcomp_1.html#T16" title="RCOMP_1:th.16">RCOMP_1:16</a></i>;<br/><a NAME="E3:49_1_1_1_1"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 <b>by </b><i><a class="ref" href="borsuk_1.html#T86" title="BORSUK_1:th.86">BORSUK_1:86</a></i>;<br/><a NAME="E4:49_1_1_1_1"/><b>then </b><i><font color="Green" title="E25">A2</font></i>: 
 <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="topmetr.html#T31" title="TOPMETR:th.31">TOPMETR:31</a></i>;<br/><a NAME="E5:49_1_1_1_1"/><b>then </b><i><font color="Green" title="E26">A3</font></i>: 
 <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font></span>)</span>
 <b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="topmetr.html#T27" title="TOPMETR:th.27">TOPMETR:27</a>, <a class="ref" href="treal_1.html#T11" title="TREAL_1:th.11">TREAL_1:11</a></i>;<br/><a NAME="E6:49_1_1_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> 
 <b>by </b><i><a class="ref" href="borsuk_1.html#T35" title="BORSUK_1:th.35">BORSUK_1:35</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c4">g</font> =  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <b>by </b><i><a class="txt" href="borsuk_2.html#E4:49_1_1_1_1"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="funct_2.html#T9" title="FUNCT_2:th.9">FUNCT_2:9</a>, <a class="ref" href="topmetr.html#T27" title="TOPMETR:th.27">TOPMETR:27</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">g</font> = <font color="Maroon" title="c4">g</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  ;<br/><b>take </b>
<font color="Maroon" title="c5">g</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1" target="_self" title="BORSUK_2:def.1">BORSUK_2:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">g</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )</span><br/><b>thus </b><a NAME="E9:49_1_1_1_1"/>
<font color="Maroon" title="c5">g</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>by </b><i><a class="txt" href="borsuk_2.html#E5:49_1_1_1_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="topmetr.html#T7" title="TOPMETR:th.7">TOPMETR:7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )</span><br/><a NAME="E10:49_1_1_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1
 <b>by </b><i><a class="ref" href="treal_1.html#D1" title="TREAL_1:def.1">TREAL_1:def 1</a></i>;<br/><b>hence </b><font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
 <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="treal_1.html#T12" title="TREAL_1:th.12">TREAL_1:12</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font>
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="treal_1.html#D1" title="TREAL_1:def.1">TREAL_1:def 1</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font></span><br/><a NAME="E12:49_1_1_1_1"/>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1 <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> 
 <b>by </b><i><a class="ref" href="treal_1.html#D2" title="TREAL_1:def.2">TREAL_1:def 2</a></i>;<br/><b>hence </b><font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> 
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="treal_1.html#T12" title="TREAL_1:th.12">TREAL_1:12</a></i>
<br/>.= 
<font color="Maroon" title="c2">b</font>
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="treal_1.html#D2" title="TREAL_1:def.2">TREAL_1:def 2</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_1_2"><b>suppose </b></a><a NAME="E1:49_1_1_1_2"/><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a> </span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c3">B</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <b>by </b><i><a class="ref" href="borsuk_1.html#T83" title="BORSUK_1:th.83">BORSUK_1:83</a>, <a class="ref" href="rcomp_1.html#T15" title="RCOMP_1:th.15">RCOMP_1:15</a>, <a class="ref" href="rcomp_1.html#T16" title="RCOMP_1:th.16">RCOMP_1:16</a></i>;<br/><a NAME="E3:49_1_1_1_2"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 <b>by </b><i><a class="ref" href="borsuk_1.html#T86" title="BORSUK_1:th.86">BORSUK_1:86</a></i>;<br/><a NAME="E4:49_1_1_1_2"/><b>then </b><i><font color="Green" title="E25">A5</font></i>: 
 <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_2"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="topmetr.html#T31" title="TOPMETR:th.31">TOPMETR:31</a></i>;<br/><a NAME="E5:49_1_1_1_2"/><b>then </b><i><font color="Green" title="E26">A6</font></i>: 
 <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font></span>)</span>
 <b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_2"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="topmetr.html#T27" title="TOPMETR:th.27">TOPMETR:27</a>, <a class="ref" href="treal_1.html#T11" title="TREAL_1:th.11">TREAL_1:11</a></i>;<br/><a NAME="E6:49_1_1_1_2"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> 
 <b>by </b><i><a class="ref" href="borsuk_1.html#T35" title="BORSUK_1:th.35">BORSUK_1:35</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c4">g</font> =  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <b>by </b><i><a class="txt" href="borsuk_2.html#E4:49_1_1_1_2"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="funct_2.html#T9" title="FUNCT_2:th.9">FUNCT_2:9</a>, <a class="ref" href="topmetr.html#T27" title="TOPMETR:th.27">TOPMETR:27</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">g</font> = <font color="Maroon" title="c4">g</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  ;<br/><a NAME="E9:49_1_1_1_2"/><i><font color="Green" title="E27">A7</font></i>: 
<font color="Maroon" title="c5">g</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>by </b><i><a class="txt" href="borsuk_2.html#E5:49_1_1_1_2"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="topmetr.html#T7" title="TOPMETR:th.7">TOPMETR:7</a></i>;<br/><a NAME="E10:49_1_1_1_2"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1
 <b>by </b><i><a class="ref" href="treal_1.html#D1" title="TREAL_1:def.1">TREAL_1:def 1</a></i>;<br/><b>then </b><i><font color="Green" title="E28">A8</font></i>: <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
 <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_2"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="treal_1.html#T12" title="TREAL_1:th.12">TREAL_1:12</a></i>
<br/>.= 
<font color="Maroon" title="c2">b</font>
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_2"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="treal_1.html#D1" title="TREAL_1:def.1">TREAL_1:def 1</a></i>
;<br/><a NAME="E12:49_1_1_1_2"/>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1 <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> 
 <b>by </b><i><a class="ref" href="treal_1.html#D2" title="TREAL_1:def.2">TREAL_1:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E29">A9</font></i>: <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> 
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_2"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="treal_1.html#T12" title="TREAL_1:th.12">TREAL_1:12</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font>
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:49_1_1_1_2"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="treal_1.html#D2" title="TREAL_1:def.2">TREAL_1:def 2</a></i>
;<br/><a NAME="E14:49_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font> <a href="borsuk_2.html#R2" title="BORSUK_2:pred.2">are_connected</a> 
 <b>by </b><i><a class="txt" href="borsuk_2.html#E9:49_1_1_1_2"><i><font color="Green" title="E27">A7</font></i></a>, <a class="txt" href="borsuk_2.html#E11:49_1_1_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="borsuk_2.html#D1" target="_self" title="BORSUK_2:def.1">Def1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c6">P</font> = <font color="Maroon" title="c5">g</font> as    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font> <b>by </b><i><a class="txt" href="borsuk_2.html#E9:49_1_1_1_2"><i><font color="Green" title="E27">A7</font></i></a>, <a class="txt" href="borsuk_2.html#E11:49_1_1_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="borsuk_2.html#E13:49_1_1_1_2"><i><font color="Green" title="E29">A9</font></i></a>, <a class="ref" href="borsuk_2.html#D2" target="_self" title="BORSUK_2:def.2">Def2</a></i>;<br/><b>take </b><font color="Maroon" title="c7">h</font> =  <a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <font color="Maroon" title="c6">P</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1" target="_self" title="BORSUK_2:def.1">BORSUK_2:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">h</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; <font color="Maroon" title="c7">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c7">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )</span><br/><a NAME="E16:49_1_1_1_2"/>
 ex <font color="Olive" title="b1">t</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  st <br/>( <font color="Olive" title="b1">t</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; <font color="Olive" title="b1">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b1">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )
 <b>by </b><i><a class="txt" href="borsuk_2.html#E9:49_1_1_1_2"><i><font color="Green" title="E27">A7</font></i></a>, <a class="txt" href="borsuk_2.html#E11:49_1_1_1_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="borsuk_2.html#E13:49_1_1_1_2"><i><font color="Green" title="E29">A9</font></i></a>, <a class="ref" href="borsuk_2.html#T18" target="_self" title="BORSUK_2:th.18">Th18</a></i>;<br/><a NAME="E17:49_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="borsuk_2.html#R2" title="BORSUK_2:pred.2">are_connected</a> 
 <b>by </b><i><a class="ref" href="borsuk_2.html#D1" target="_self" title="BORSUK_2:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E18:49_1_1_1_2"/>
( <font color="Maroon" title="c7">h</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; <font color="Maroon" title="c7">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c7">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )
 <b>by </b><i><a class="ref" href="borsuk_2.html#D2" target="_self" title="BORSUK_2:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
