complete lattice homomorphism
Complete lattice homomorphism is a function from one lattice^{} to an other lattice, which preserves arbitrary (not only finite) meets and joins.
If $\varphi :L\to M$ is lattice homomorphism^{} between complete^{} lattices $L$ and $M$ such that

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$\varphi (\bigvee \{{a}_{i}\mid i\in I\})=\bigvee \{\varphi ({a}_{i})\mid i\in I\}$, and

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$\varphi (\bigwedge \{{a}_{i}\mid i\in I\})=\bigwedge \{\varphi ({a}_{i})\mid i\in I\}$,
then $\varphi $ is called a complete lattice homomorphism.
Most often are considered complete lattice homomorphisms from one complete lattice^{} 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  20130322 16:58:02 
Last modified on  20130322 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 