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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:76_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><div><i><font color="Green">E30</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:76_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon">c<sub>4</sub></font> =  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><a NAME="E1:76_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="tex_2.html#E1:76_1_1"><i><font color="Green">E31</font></i></a></i>;<br/></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:76_1_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon">c<sub>4</sub></font> =  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><a NAME="E1:76_1_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="tex_2.html#E1:76_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/></div>
<b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:76_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K9">/\</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="tex_2.html#E1:76_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="tex_2.html#E2:76_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="zfmisc_1.html#T39">ZFMISC_1:39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:76"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> is <a href="tex_2.html#V3" target="_self">discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D5" target="_self">Def5</a></i>;<br/>


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