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<b>let </b><font color="Maroon">T</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">F</font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:6"/>
 ex <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">A</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">A</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E3:6"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">A</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>take </b><font color="Maroon">O</font> =  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>;<br/><a NAME="E1:6_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 ;<br/><b>hence </b><a NAME="E2:6_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font>
 <b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>assume </b><a NAME="E1:6_1_1"/>
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 ;<br/><a NAME="E2:6_1_1"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">B</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">A</font></span><a href="domain_1.html#K6">}</a></span> &amp; <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">C</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">A</font></span><a href="domain_1.html#K6">}</a></span> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><a NAME="E3:6_1_1"/><b>then </b>
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T6">ZFMISC_1:6</a></i>;<br/><b>hence </b><a NAME="E4:6_1_1"/>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:6_1"/>
for <font color="Olive">B</font>, <font color="Olive">C</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Olive">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">O</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">B</font> &amp; <font color="Maroon">O</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">C</font> holds <br/><font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">C</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon">F</font> is <a href="nagata_1.html#V1" target="_self">discrete</a>
 <b>by </b><i/>;<br/>


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