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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c1">X</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="c2">Y</font><br/> for <font color="Olive" title="b3">V</font> being   <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b4">W</font> being   <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Olive" title="b2">B</font> holds  <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Olive" title="b3">V</font>,<font color="Olive" title="b4">W</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c2">Y</font><br/> for <font color="Olive" title="b2">V</font> being   <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b3">W</font> being   <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Olive" title="b1">B</font> holds  <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">W</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Olive" title="b1">B</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V</font> being   <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b2">W</font> being   <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c4">B</font> holds  <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">V</font> be    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c4">B</font> holds  <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">V</font>,<font color="Olive" title="b1">W</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">W</font> be    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <font color="Maroon" title="c4">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">V</font>,<font color="Maroon" title="c6">W</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> is    <a href="connsp_2.html#M2" title="CONNSP_2:mode.2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span></span><br/>











<a NAME="E1:57"/>
( <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c5">V</font> &amp; <font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c6">W</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_2.html#D2" title="CONNSP_2:def.2">CONNSP_2:def 2</a></span>;<br/>
<a NAME="E2:57"/><span class="kw">then </span>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c5">V</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c6">W</font></span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:57"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">V</font>,<font color="Maroon" title="c6">W</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T47" target="_self" title="BORSUK_1:th.47">Th47</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="connsp_2.html#D2" title="CONNSP_2:def.2">CONNSP_2:def 2</a> <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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