We introduce r -fuzzy strongly preopen and r -fuzzy strongly preclosed sets in fuzzy topological space in view of the definition of Šostak (1985). We investigate some properties of them. Moreover, the concepts of fuzzy SP-continuous, fuzzy SP-irresolute continuous, fuzzy SP-irresolute open (closed) mappings, and a fuzzy SP-irresolute homeomorphism are introduced and studied. Some of their chara...

In this paper, the theory of Oθ-convergence and weak Oθ-convergence of nets is introduced in L-spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shi’s O-convergence. It can be used to characterize preclosed sets, preopen sets, θ-closed sets, θ-open sets, almost F -compactness and almost S-compactness.

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

A new notion of SP-compactness is introduced in L-topological spaces by means of semi-preopen L-sets and their inequality, where L is a complete De Morgan algebra. This new notion does not depend on the structure of basis lattice L and L does not require any distributivity. This new notion implies semicompactness, hence it also implies compactness. This new notion is a good extension and it has...