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<b>let </b><font color="Maroon" title="c1">X</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="borsuk_1.html#K12" title="BORSUK_1:func.12">TrivDecomp</a> <font color="Maroon" title="c1">X</font> is    <a href="borsuk_1.html#M1" title="BORSUK_1:mode.1">u.s.c._decomposition</a> of <font color="Maroon" title="c1">X</font></span><br/>

<b>thus </b><a NAME="E1:87"/>
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>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="borsuk_1.html#K12" title="BORSUK_1:func.12">TrivDecomp</a> <font color="Maroon" title="c1">X</font> holds <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="Olive" title="b1">A</font>  ex <font color="Olive" title="b3">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b3">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">W</font> &amp; <font color="Olive" title="b3">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> &amp; ( for <font color="Olive" title="b4">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b4">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="borsuk_1.html#K12" title="BORSUK_1:func.12">TrivDecomp</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b4">B</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b3">W</font> holds <br/><font color="Olive" title="b4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">W</font> ) )
 <b>by </b><i><a class="txt" href="borsuk_1.html#E78"><i><font color="Green" title="E52">Lm1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_1.html#D13" target="_self" title="BORSUK_1:def.13">BORSUK_1:def 13</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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