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<span class="kw">let </span><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 <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="borsuk_2.html#D3" title="BORSUK_2:def.3">BORSUK_2:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">a1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c9">a2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font><span class="kw"> such that </span><br/><a NAME="E2:23_1_1"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[</a><span class="default"><font color="Maroon" title="c8">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T50" title="BORSUK_1:th.50">BORSUK_1:50</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">b1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c11">b2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font><span class="kw"> such that </span><br/><a NAME="E4:23_1_1"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[</a><span class="default"><font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">b2</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T50" title="BORSUK_1:th.50">BORSUK_1:50</a></span>;<br/>
<a NAME="E5:23_1_1"/>
( <font color="Maroon" title="c8">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c11">b2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_2.html#D3" title="BORSUK_2:def.3">BORSUK_2:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:23_1_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</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="#E2:23_1_1"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E4:23_1_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="topalg_4.html#T15" target="_self" title="TOPALG_4:th.15">Th15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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