join

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 $j^{\prime}$ are both joins of $x$ and $y$, then $j\leq j^{\prime}$ and $j^{\prime}\leq j$, and so $j=j^{\prime}$; thus a join, if it exists, is unique. The join is also known as the or operator.

 Title join Canonical name Join Date of creation 2013-03-22 12:27:40 Last modified on 2013-03-22 12:27:40 Owner yark (2760) Last modified by yark (2760) Numerical id 11 Author yark (2760) Entry type Definition Classification msc 06A12 Synonym or operator Related topic Meet Related topic Semilattice Defines join-semilattice Defines join semilattice Defines upper semilattice