# Definition:Meet Semilattice

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## 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

### Generalizations

## Sources

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