Definition:Meet Semilattice/Definition 1

Definition

Let $\struct {S, \preceq}$ be an ordered set.

Suppose that for all $a, b \in S$:

$a \wedge b \in S$,

where $a \wedge b$ is the meet of $a$ and $b$.

Then the ordered structure $\struct {S, \wedge, \preceq}$ is called a meet semilattice.

Also see

• Equivalence of Definitions of Meet Semilattice

• Definition:Join Semilattice

• Meet Semilattice is Ordered Structure

• Meet Semilattice is Semilattice

• Results about meet semilattices can be found here.

Sources

• Semi-lattice. Encyclopedia of Mathematics. URL: https://www.encyclopediaofmath.org/index.php?title=Semi-lattice&oldid=39737