join

Certain posets $X$ have a binary operation join denoted by $\vee$, such that $x\vee y$ is the least upper bound of $x$ and $y$. Such posets are called join-semilattices, or $\mathrm{\vee }$-semilattices, or upper semilattices.

If $j$ and $j^{\prime }$ are both joins of $x$ and $y$, then $j\le j^{\prime }$ and $j^{\prime }\le j$, 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