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