# closed sublattice

A sublattice $K$ of a complete lattice $L$ is a 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.

Title closed sublattice ClosedSublattice 2013-03-22 18:57:28 2013-03-22 18:57:28 porton (9363) porton (9363) 5 porton (9363) Definition msc 06B23 Sublattice Lattice