Definition:Meet Irreducible

Definition

Let $\left({S, \wedge, \preceq}\right)$ be a meet semilattice.

Let $g \in S$.

Then $g$ is meet irreducible if and only if:

$\forall x, y \in S: g = x \wedge y \implies g = x$ or $g = y$

Sources

• 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices

• Mizar article WAYBEL_6:def 2