Definition:Dense (Lattice Theory)/Subset

Definition

Let $L = \struct {S, \wedge, \preceq}$ be a bounded below meet semilattice.

Let $A$ be a subset of $S$.

Then $A$ is dense if and only if it includes only dense elements.

That means that if and only if $\forall x \in A: x$ is a dense element.

Sources

• Mizar article WAYBEL12:def 5