Definition:Meet Semilattice

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 known as
A meet semilattice is also known as a lower semilattice.

Also see

 * Definition:Join Semilattice


 * Meet Semilattice is Ordered Structure
 * Meet Semilattice is Semilattice

Generalizations

 * Definition:Semilattice