Definition:Compact Subset of Lattice

Definition

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

Compact subset of $S$, denoted $\map K L$, equals to the set of all compact elements of $S$.

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_8:def 1