Definition:Join Semilattice/Definition 1

Definition
Let $\struct {S, \preceq}$ be an ordered set.

Suppose that for all $a, b \in S$:


 * $a \vee b \in S$

where $a \vee b$ is the join of $a$ and $b$ with respect to $\preceq$.

Then the ordered structure $\struct {S, \vee, \preceq}$ is called a join semilattice.

Also see

 * Definition:Meet Semilattice
 * Definition:Semilattice