Abstract: In L-topological spaces, γ-open L-sets were introduced and the definition of γ-compactness was presented by inequality, where L was a complete DeMorgan algebra. This definition does not rely on the structure of basic lattice L and no distributivity was required in L. It was characterized by means of γ-closed L-sets and their inequality. The further characterizations of γ-compactness were discussed when L is a completely distributive DeMorgan algebra.

Key words: γ-compactness , γ-open L-sets, L-topology