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complete lattice homomorphism
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(Definition)
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Complete lattice homomorphism is a function from one lattice to an other lattice, which preserves arbitrary (not only finite) meets and joins.
If $\phi:L \to M$ is lattice homomorphism between complete lattices $L$ and $M$ such that
- $\phi(\bigvee \lbrace a_i\mid i\in I\rbrace) = \bigvee \lbrace \phi(a_i)\mid i\in I\rbrace$ and
- $\phi(\bigwedge \lbrace a_i\mid i\in I\rbrace) = \bigwedge \lbrace \phi(a_i)\mid i\in I\rbrace$
then $\phi$ 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.
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"complete lattice homomorphism" is owned by porton.
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Cross-references: complete lattice, complete, lattice homomorphism, joins, meets, finite, preserves, lattice, function
There are 4 references to this entry.
This is version 3 of complete lattice homomorphism, born on 2007-04-22, modified 2007-05-27.
Object id is 9241, canonical name is CompleteLatticeHomomorphism.
Accessed 1071 times total.
Classification:
| AMS MSC: | 06B23 (Order, lattices, ordered algebraic structures :: Lattices :: Complete lattices, completions) |
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Pending Errata and Addenda
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