In this paper we have introduced the concept of (γ, γ′)-preopen sets in topological space.

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.

The goal of this paper is to investigate the certain properties bipolar fuzzy supra preopen sets (BF set). We introduce and study concepts pre-interior pre-interior) pre-closure pre-closure) operators. Furthermore, we define new type continuous mapping based on BF sets.

In this paper, a collection of sets are investigated in such way that the splits preopen and b-open also semi-open sets. Functions terms is part paper it will be considered these remains invariant under homeomorphic image.