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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.
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"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 52 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 11424 times total.
Classification:
| AMS MSC: | 06A12 (Order, lattices, ordered algebraic structures :: Ordered sets :: Semilattices) |
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Pending Errata and Addenda
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