<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>



<a NAME="E1:58"/><i><font color="Green" title="E44">A1</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T54" target="_self" title="BORSUK_1:th.54">Th54</a></i>;<br/>
<a NAME="E2:58"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T44" title="TOPS_1:th.44">TOPS_1:44</a></i>;<br/>
<a NAME="E3:58"/><b>then </b>
 <a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T52" target="_self" title="BORSUK_1:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E1:58"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T95" title="ZFMISC_1:th.95">ZFMISC_1:95</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<a NAME="E5:58"/>
 <a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <font color="Maroon" title="c3">A</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T51" target="_self" title="BORSUK_1:th.51">Th51</a></i>;<br/>
<a NAME="E6:58"/><b>then </b><i><font color="Green" title="E45">A2</font></i>: 
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="ref" href="tops_2.html#T26" title="TOPS_2:th.26">TOPS_2:26</a></i>;<br/>
<a NAME="E7:58"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T53" target="_self" title="BORSUK_1:th.53">Th53</a></i>;<br/>
<b>hence </b><a NAME="E8:58"/>
 <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K10" title="BORSUK_1:func.10">Base-Appr</a> <font color="Maroon" title="c3">A</font></span>)</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> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E6:58"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="tops_1.html#T56" title="TOPS_1:th.56">TOPS_1:56</a></i>;<br/>


</div>
