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meet (Definition)

Certain posets $ X$ have a binary operation meet denoted by $ \land$, such that $ x \land y$ is the greatest lower bound of $ x$ and $ y$. Such posets are called meet-semilattices, or $ \land$-semilattices, or lower semilattices.

If $ m$ and $ m'$ are both meets of $ x$ and $ y$, then $ m \leq m'$ and $ m \geq m'$, and so $ m = m'$; thus a meet, if it exists, is unique. The meet is also known as the and operator.



"meet" is owned by yark. [ full author list (2) | owner history (1) ]
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See Also: join, semilattice

Other names:  and operator
Also defines:  meet-semilattice, meet semilattice, lower semilattice
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Cross-references: meets, greatest lower bound, binary operation, posets
There are 47 references to this entry.

This is version 7 of meet, born on 2002-02-24, modified 2005-02-26.
Object id is 2610, canonical name is Meet.
Accessed 9391 times total.

Classification:
AMS MSC: 06A12 (Order, lattices, ordered algebraic structures :: Ordered sets :: Semilattices)
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