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Certain posets $X$ have a binary operation join denoted by $\lor$ such that $x \lor y$ is the least upper bound of $x$ and $y$ Such posets are called join-semilattices, or $\lor$ semilattices, or upper semilattices.
If $j$ and $j'$ are both joins of $x$ and $y$ then $j \leq j'$ and $j' \leq j$ and so $j = j'$ thus a join, if it exists, is unique. The join is also known as the or operator.
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"join" is owned by yark. [ full author list (2) | owner history (1) ]
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See Also: meet, semilattice
| Also defines: |
join-semilattice, join semilattice, upper semilattice |
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Cross-references: least upper bound, binary operation, posets
There are 57 references to this entry.
This is version 8 of join, born on 2002-02-24, modified 2005-02-26.
Object id is 2611, canonical name is Join.
Accessed 9436 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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