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<b>let </b><font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c5">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">S</font><br/> for <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">T</font>  st <font color="Olive" title="b1">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> &amp; <font color="Olive" title="b2">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> holds <br/><span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a></span><br/><b>let </b><font color="Maroon" title="c6">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">T</font>  st <font color="Maroon" title="c6">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> &amp; <font color="Olive" title="b1">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> holds <br/><span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Olive" title="b1">B</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a></span><br/><b>let </b><font color="Maroon" title="c7">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> &amp; <font color="Maroon" title="c7">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> implies <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )</span><br/>





<b>assume </b><a NAME="E1:20"/>
( <font color="Maroon" title="c4">S</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a> &amp; <font color="Maroon" title="c5">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c7">B</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_1.html#D3" title="CONNSP_1:def.3">CONNSP_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c8">SA</font> = <font color="Maroon" title="c4">S</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">A</font>, <font color="Maroon" title="c9">TB</font> = <font color="Maroon" title="c5">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c7">B</font> as  <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> ;<br/>
<a NAME="E3:20"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c8">SA</font>,<font color="Maroon" title="c9">TB</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 
;<br/>
<b>hence </b><a NAME="E4:20"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="borsuk_3.html#T26" title="BORSUK_3:th.26">BORSUK_3:26</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_1.html#D3" title="CONNSP_1:def.3">CONNSP_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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