Max Semigroup on Toset forms Semilattice

Theorem

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

Then the max semigroup $\struct {S, \max}$ is a semilattice.

Proof

The Max Semigroup is Commutative and idempotent.

Hence the result, by definition of a semilattice.

$\blacksquare$

Also see

• Min Semigroup on Toset forms Semilattice