In this paper the authors introduce and characterize r-open, r-semiopen sets (resp. r-closed, r-semiclosed sets) and open, semiopen and semi-continuous maps (resp. closed, semiclosed maps) in L-fuzzy closure spaces.
The concepts of γ-compactness, countable γ-compactness, the γ-Lindelöf property are introduced in L-topological spaces by means of γ-open L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required.