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<div><span class="kw">theorem </span><a NAME="T35"><span class="comment"><font color="firebrick">:: WAYBEL14:35</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b1">L</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  holds <br/> ex <font color="Olive" title="b3">B</font> being   <a href="yellow_8.html#NM1" title="YELLOW_8:NM.1">Basis</a> of <font color="Olive" title="b2">x</font> st <br/> for <font color="Olive" title="b4">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b4">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">B</font> holds <br/>( <font color="Olive" title="b4">X</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive" title="b4">X</font> is  <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a>  )</div></div>
