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<b>let </b><font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c5">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>;<br/><b>let </b><font color="Maroon" title="c8">t1</font>, <font color="Maroon" title="c9">t2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font>;<br/>











<b>given </b><font color="Maroon" title="c10">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="borsuk_1.html#K20" title="BORSUK_1:func.20">I[01]</a> ,<font color="Maroon" title="c4">S</font><b> such that </b><a NAME="E2:19"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c10">f</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>and </b><br/><a NAME="E3:19"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c10">f</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="c6">s1</font>
 <b>and </b><br/><a NAME="E4:19"/><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c10">f</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="c7">s2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1" title="BORSUK_2:def.1">BORSUK_2:def 1</a><br/>

<b>given </b><font color="Maroon" title="c11">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="borsuk_1.html#K20" title="BORSUK_1:func.20">I[01]</a> ,<font color="Maroon" title="c5">T</font><b> such that </b><a NAME="E6:19"/><i><font color="Green" title="E21">A4</font></i>: 
<font color="Maroon" title="c11">g</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>and </b><br/><a NAME="E7:19"/><i><font color="Green" title="E22">A5</font></i>: 
<font color="Maroon" title="c11">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="c8">t1</font>
 <b>and </b><br/><a NAME="E8:19"/><i><font color="Green" title="E23">A6</font></i>: 
<font color="Maroon" title="c11">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="c9">t2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1" title="BORSUK_2:def.1">BORSUK_2:def 1</a><br/>

<b>take </b>
<span class="p1"><a href="topalg_4.html#K3" title="TOPALG_4:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c11">g</font></span><a href="topalg_4.html#K3" title="TOPALG_4:func.3">:&gt;</a></span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1" title="BORSUK_2:def.1">BORSUK_2:def 1</a><br/>

<b>thus </b><a NAME="E9:19"/>
<span class="p1"><a href="topalg_4.html#K3" title="TOPALG_4:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c11">g</font></span><a href="topalg_4.html#K3" title="TOPALG_4:func.3">:&gt;</a></span> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>by </b><i><a class="txt" href="topalg_4.html#E2:19"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="topalg_4.html#E6:19"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="yellow12.html#T41" title="YELLOW12:th.41">YELLOW12:41</a></i>;<br/>

<a NAME="E10:19"/><i><font color="Green" title="E24">A7</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="borsuk_1.html#K20" title="BORSUK_1:func.20">I[01]</a>  &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c11">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="borsuk_1.html#K20" title="BORSUK_1:func.20">I[01]</a>  )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><span class="p1"><a href="topalg_4.html#K3" title="TOPALG_4:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c11">g</font></span><a href="topalg_4.html#K3" title="TOPALG_4:func.3">:&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">j0</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">j0</font></span>)</span></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>
<b>by </b><i><a class="ref" href="funct_3.html#T69" title="FUNCT_3:th.69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c8">t1</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E3:19"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="topalg_4.html#E7:19"><i><font color="Green" title="E22">A5</font></i></a></i>
;<br/><br/>

<b>thus </b><span class="p1"><a href="topalg_4.html#K3" title="TOPALG_4:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c11">g</font></span><a href="topalg_4.html#K3" title="TOPALG_4:func.3">:&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">j1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">j1</font></span>)</span></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E10:19"><i><font color="Green" title="E24">A7</font></i></a>, <a class="ref" href="funct_3.html#T69" title="FUNCT_3:th.69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c9">t2</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E4:19"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="topalg_4.html#E8:19"><i><font color="Green" title="E23">A6</font></i></a></i>
;<br/>


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