meet

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

 Title meet Canonical name Meet Date of creation 2013-03-22 12:27:37 Last modified on 2013-03-22 12:27:37 Owner yark (2760) Last modified by yark (2760) Numerical id 10 Author yark (2760) Entry type Definition Classification msc 06A12 Synonym and operator Related topic Join Related topic Semilattice Defines meet-semilattice Defines meet semilattice Defines lower semilattice