Definition:Bounded Lattice/Definition 1

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Suppose that $S$ admits all finite suprema and finite infima.

Denote by $\vee$ and $\wedge$ the join and meet operations on $S$, respectively.

Then the ordered structure $\left({S, \vee, \wedge, \preceq}\right)$ is called a bounded lattice.

Also see

 * Lattice