closed sublatticeClosedSublattice2009-06-09 11:15:532009-06-13 11:13:06Definition% this is the default PlanetMath preamble. as your knowledge
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A sublattice $K$ of a complete lattice $L$ is a \emph{closed sublattice} of $L$ iff $K$ contains the meet and the join of any its nonempty subset.
Examples:
Any complete sublattice is a closed sublattice.
$[0;1]$ is a closed sublattice of $(-\infty;\infty)$.
The set of rational numbers is not a closed sublattice of the set of real numbers.