Lattice

Let $𝑆$ be a poset. Then iff for every $𝑎, 𝑏 \in 𝑆$ #m/def/order

there exists a join $𝑎 \land 𝑏$ , then $𝑆$ is called a join-semilattice.
there exists a meet $𝑎 \lor 𝑏$ , then $𝑆$ is called a meet-semillatice.
there exists both a join and a meet, then $𝑆$ is called a lattice.

Iff they exist for arbitrary collections of objects then it is said to be a Complete lattice.

See also

Not to be confused with Lattice subgroup

#state/develop | #lang/en | #SemBr