closed sublattice

A sublattice K of a complete latticeMathworldPlanetmath L is a closed sublattice of L iff K contains the meet and the join of any its nonempty subset.


Any completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath sublattice is a closed sublattice.

[0;1] is a closed sublattice of (-;).

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