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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">D</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>assume </b><a NAME="E1:75_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">D</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">G</font> =  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">X</font>;<br/><b>thus </b><a NAME="E1:75_1_1"/>
( <font color="Maroon">G</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> )
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:75_1"/>
 ex <font color="Olive">G</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">G</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:75"/>
<font color="Maroon">A</font> is <a href="tex_2.html#V3" target="_self">discrete</a>
 <b>by </b><i/>;<br/>


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