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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:79"/><i><font color="Green" title="E30">A1</font></i>: 
( <font color="Maroon" title="c2">A</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 ;<br/>

<b>assume </b><a NAME="E2:79"/><i><font color="Green" title="E31">A2</font></i>: 
( <font color="Maroon" title="c2">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">discrete</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">discrete</a> )
 ;<br/>

<a NAME="E3:79"/>
for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</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">P</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Olive" title="b2">Q</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> holds <br/>( <font color="Olive" title="b1">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Q</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Olive" title="b1">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">Q</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 
<b>by </b><i><a class="ref" href="tops_1.html#T35" title="TOPS_1:th.35">TOPS_1:35</a>, <a class="ref" href="tops_1.html#T36" title="TOPS_1:th.36">TOPS_1:36</a></i>;<br/>
<b>hence </b><a NAME="E4:79"/>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">discrete</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:79"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="tex_2.html#E2:79"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="tex_2.html#T31" target="_self" title="TEX_2:th.31">Th31</a></i>;<br/>


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