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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<a NAME="E1:35"/><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1" target="_self">{}</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E2:35"/>
 <a href="pre_topc.html#K1" target="_self">{}</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E3:35"/><b>then </b>
 <a href="pre_topc.html#K1" target="_self">{}</a> <font color="Maroon">c<sub>1</sub></font> is <a href="pre_topc.html#V3" target="_self">open</a>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E4:35"/>
 <a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>1</sub></font> is <a href="pre_topc.html#V4" target="_self">closed</a>
 <b>by </b><i><a class="txt" href="pre_topc.html#E1:35"><i><font color="Green">E15</font></i></a>, <a class="ref" href="pre_topc.html#D6" target="_self">Def6</a></i>;<br/>


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