Pseudo-closure operators in fuzzy neighbourhood-base spaces

Abstract

Fuzzy neighbourhood-base spaces and dual fuzzy neighbourhood spaces are two special types of fuzzy topological spaces. They were introduced by Morsi as useful tools for the theory, explanation and application of Lowen's fuzzy neighbourhood systems. The notion of the pseudoclosure operator of a fuzzy topological space was introduced by Mashhour et al. as a tool in establishing a necessary and sufficient condition for the productivity of fuzzy Kuratowski operators. Pseudo-closure operators carry partial information about the fuzzy closure operators of their respective spaces. We establish relationships between the pseudo-closure operators of fuzzy neighbourhood-base spaces, their fuzzy closure operators and their level topologies. We provide counterexamples to disprove other nonvalid relationships. We also study some categorical aspects of the operation of taking the pseudo-closure operators of fuzzy topological spaces.