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 $(-\mathrm{\infty };\mathrm{\infty })$.

The set of rational numbers is not a closed sublattice of the set of real numbers.

Title	closed sublattice
Canonical name	ClosedSublattice
Date of creation	2013-03-22 18:57:28
Last modified on	2013-03-22 18:57:28
Owner	porton (9363)
Last modified by	porton (9363)
Numerical id	5
Author	porton (9363)
Entry type	Definition
Classification	msc 06B23
Related topic	Sublattice
Related topic	Lattice