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<b>let </b><font color="Maroon" title="c5">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:12_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c5">T</font> is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D3" title="BORSUK_2:def.3">BORSUK_2:def 3</a><br/>

<b>take </b><font color="Maroon" title="c8">f</font> = <a href="borsuk_1.html#K20" title="BORSUK_1:func.20">I[01]</a>  <a href="borsuk_1.html#K3" title="BORSUK_1:func.3">--&gt;</a> <font color="Maroon" title="c6">a</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>thus </b><a NAME="E2:12_1_1"/>
<font color="Maroon" title="c8">f</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 ;<br/>

<a NAME="E3:12_1_1"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="topalg_3.html#E1:12_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="realset2.html#D7" title="REALSET2:def.7">REALSET2:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:12_1_1"/>
( <font color="Maroon" title="c8">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c8">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">b</font> )
 <b>by </b><i><a class="ref" href="topalg_3.html#T5" target="_self" title="TOPALG_3:th.5">Th5</a>, <a class="ref" href="borsuk_1.html#D17" title="BORSUK_1:def.17">BORSUK_1:def 17</a>, <a class="ref" href="borsuk_1.html#D18" title="BORSUK_1:def.18">BORSUK_1:def 18</a></i>;<br/>


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