Equivalence among some neighborhood structures in fuzzy topology

Abstract

We deepen the study of two known neighborhood structures, which here will be called f⋅k-neighborhood structures and f⋅q-neighborhood structures, in the context of Šostak fuzzy topological spaces. In particular, we characterize fuzzy topologies by f⋅k-neighbor-hood structures. Moreover we introduce and discuss the notions of f⋅k-neighborhood prestructure and f⋅m-neighborhood structure in the same context. At last we prove that the three neighborhood structures mentioned above are equivalent.