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<b>let </b><font color="Maroon" title="c1">TS</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">TS</font> <a href="compts_1.html#NR2" title="COMPTS_1:NR.2">is_T2</a> 
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c1">TS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">TS</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="compts_1.html#D5" target="_self" title="COMPTS_1:def.5">COMPTS_1:def 5</a><br/><b>let </b><font color="Maroon" title="c3">F</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E3:18"/><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>and </b><br/><a NAME="E4:18"/><i><font color="Green" title="E18">A4</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E5:18"/><i><font color="Green" title="E19">A5</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 ;<br/>

<a NAME="E6:18"/>
<font color="Maroon" title="c3">F</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 
<b>by </b><i><a class="txt" href="compts_1.html#E2:18"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="compts_1.html#E4:18"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="compts_1.html#T17" target="_self" title="COMPTS_1:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E7:18"/>
 ex <font color="Olive" title="b1">W</font>, <font color="Olive" title="b2">V</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font> st <br/>( <font color="Olive" title="b1">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Olive" title="b2">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> &amp; <font color="Olive" title="b1">W</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">V</font> )
 <b>by </b><i><a class="txt" href="compts_1.html#E1:18"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="compts_1.html#E3:18"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="compts_1.html#E5:18"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="compts_1.html#T15" target="_self" title="COMPTS_1:th.15">Th15</a></i>;<br/>


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