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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">X0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c5">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X0</font>;<br/>







<b>assume </b><a NAME="E1:59"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font>
 ;<br/>

<a NAME="E2:59"/><b>then </b><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c4">C</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="ref" href="tsep_1.html#D1" title="TSEP_1:def.1">TSEP_1:def 1</a></i>;<br/>
<b>assume </b><a NAME="E3:59"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font>
 ;<br/>

<b>hence </b><a NAME="E4:59"/>
( ( <font color="Maroon" title="c4">C</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> &amp; <font color="Maroon" title="c5">B</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> ) iff <font color="Maroon" title="c3">A</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> )
 <b>by </b><i><a class="txt" href="tops_3.html#E1:59"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="tops_3.html#E2:59"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="tops_3.html#T62" target="_self" title="TOPS_3:th.62">Th62</a></i>;<br/>


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