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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>thus </b><a NAME="E1:91"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_1.html#K13" target="_self">TrivDecomp</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="connsp_2.html#M2">a_neighborhood</a> of <font color="Olive">b<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="borsuk_1.html#K13" target="_self">TrivDecomp</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">b<sub>3</sub></font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>3</sub></font> ) )
 <b>by </b><i><a class="txt" href="borsuk_1.html#E78"><i><font color="Green">Lemma55</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_1.html#D13" target="_self">BORSUK_1:def 13</a><br/>


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