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<b>let </b><font color="Maroon">X</font> be   <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">Y</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="borsuk_1.html#K5" target="_self">:]</a></span>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K5" target="_self">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="borsuk_1.html#K5" target="_self">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1">TOPS_2:def 1</a><br/>





<b>assume </b><a NAME="E1:55"/>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:55"/><b>then </b>
 ex <font color="Olive">X1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> ex <font color="Olive">Y1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font> st <br/>( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><font color="Olive">X1</font>,<font color="Olive">Y1</font></span><a href="borsuk_1.html#K6" target="_self">:]</a></span> &amp; <span class="p1"><a href="borsuk_1.html#K6" target="_self">[:</a><span class="default"><font color="Olive">X1</font>,<font color="Olive">Y1</font></span><a href="borsuk_1.html#K6" target="_self">:]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Olive">X1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">Y1</font> is <a href="pre_topc.html#V3">open</a> )
 
;<br/>
<b>hence </b><a NAME="E3:55"/>
<font color="Maroon">B</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i/>;<br/>


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