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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/>



<a NAME="E1:59"/><i><font color="Green">E24</font></i>: 
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:59"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T44">TOPS_1:44</a></i>;<br/>
<a NAME="E3:59"/><b>then </b>
 <a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:59"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T95">ZFMISC_1:95</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<a NAME="E5:59"/>
 <a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <font color="Maroon">A</font> is <a href="tops_2.html#V1">open</a>
 
<b>by </b><i/>;<br/>
<a NAME="E6:59"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <font color="Maroon">A</font></span>)</span> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="tops_2.html#T26">TOPS_2:26</a></i>;<br/>
<a NAME="E7:59"/>
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:59"/>
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" target="_self">Base-Appr</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="tops_1.html#T56">TOPS_1:56</a></i>;<br/>


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