meet

Certain posets $X$ have a binary operation meet denoted by $\wedge$, such that $x\wedge y$ is the greatest lower bound of $x$ and $y$. Such posets are called meet-semilattices, or $\mathrm{\wedge }$-semilattices, or lower semilattices.

If $m$ and $m^{\prime }$ are both meets of $x$ and $y$, then $m\le m^{\prime }$ and $m\ge m^{\prime }$, 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