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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="yellow_9.html#M3" target="_self">Refinement</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>





<b>assume </b><a NAME="E1:89"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:89"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E3:89"/><b>then </b>
 <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E4:89"/>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_9.html#T22" target="_self">Th22</a></i>;<br/>


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