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<span class="kw">set </span><font color="Maroon" title="c2">t</font> =  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">f</font> = <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a>  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>;<br/>
<a NAME="E1:48_1_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
( <span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a>  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> &amp; <span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a>  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D14" onmouseover="rs('borsuk_1/D14')" onmouseout="rh()">BORSUK_1:def 14</a>, <a class="ref" href="borsuk_1.html#D15" onmouseover="rs('borsuk_1/D15')" onmouseout="rh()">BORSUK_1:def 15</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">p</font> =  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>, the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>;<br/>
<a NAME="E2:48_1_1"/>
 the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>, the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">c</font> =  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of  the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>, the   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> as   <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_6.html#T22" target="_self" onmouseover="rs('topalg_6/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">c</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">c</font> is  <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a> </span><br/>

<a NAME="E4:48_1_1"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T40" onmouseover="rs('borsuk_1/T40')" onmouseout="rh()">BORSUK_1:40</a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">S</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<a NAME="E5:48_1_1"/>
 <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_2.html#T25" onmouseover="rs('xxreal_2/T25')" onmouseout="rh()">XXREAL_2:25</a></span>;<br/>
<a NAME="E6:48_1_1"/><span class="kw">then </span>
 <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:48_1_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c5">c</font> is  <a href="xxreal_2.html#V1" title="XXREAL_2:attr.1">left_end</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48_1_1"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="xxreal_2.html#D5" onmouseover="rs('xxreal_2/D5')" onmouseout="rh()">XXREAL_2:def 5</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="topalg_6.html#D6" target="_self" onmouseover="rs('topalg_6/D6')" onmouseout="rh()">TOPALG_6:def 6</a>,<a class="ref" href="topalg_6.html#D8" target="_self" onmouseover="rs('topalg_6/D8')" onmouseout="rh()">TOPALG_6:def 8</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">c</font> is  <a href="topalg_6.html#V6" title="TOPALG_6:attr.6">with_last_point</a> </span><br/>

<a NAME="E8:48_1_1"/>
 <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_2.html#T29" onmouseover="rs('xxreal_2/T29')" onmouseout="rh()">XXREAL_2:29</a></span>;<br/>
<a NAME="E9:48_1_1"/><span class="kw">then </span>
 <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_1.html#T1" onmouseover="rs('xxreal_1/T1')" onmouseout="rh()">XXREAL_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:48_1_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c5">c</font> is  <a href="xxreal_2.html#V2" title="XXREAL_2:attr.2">right_end</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48_1_1"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="xxreal_2.html#D6" onmouseover="rs('xxreal_2/D6')" onmouseout="rh()">XXREAL_2:def 6</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="topalg_6.html#D7" target="_self" onmouseover="rs('topalg_6/D7')" onmouseout="rh()">TOPALG_6:def 7</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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