complete lattice homomorphism

Complete lattice homomorphism is a function from one latticeMathworldPlanetmath to an other lattice, which preserves arbitrary (not only finite) meets and joins.

If ϕ:LM is lattice homomorphismMathworldPlanetmath between completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath lattices L and M such that

  • ϕ({aiiI})={ϕ(ai)iI}, and

  • ϕ({aiiI})={ϕ(ai)iI},

then ϕ is called a complete lattice homomorphism.

Most often are considered complete lattice homomorphisms from one complete latticeMathworldPlanetmath to an other complete lattice (that is when all meets and joins are defined).

Complete lattice homomorphism is a special case of lattice homomorphism.

Title complete lattice homomorphism
Canonical name CompleteLatticeHomomorphism
Date of creation 2013-03-22 16:58:02
Last modified on 2013-03-22 16:58:02
Owner porton (9363)
Last modified by porton (9363)
Numerical id 6
Author porton (9363)
Entry type Definition
Classification msc 06B23
Related topic CompleteLattice