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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/><b>let </b><font color="Maroon">c<sub>2</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="E1:8"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V4">condensed</a> &amp;  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/>

<a NAME="E2:8"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V6">open_condensed</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V5">closed_condensed</a> )
 
<b>by </b><i><a class="ref" href="tdlat_3.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E3:8"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V4">closed</a> )
 <b>by </b><i><a class="ref" href="tops_1.html#T106">TOPS_1:106</a>, <a class="ref" href="tops_1.html#T107">TOPS_1:107</a></i>;<br/>


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