Fuzzy semiregularization topologies and fuzzy submaximal spaces

Abstract The aim of the paper is to investigate the fuzzy semiregularization spaces associated with fuzzy topological spaces. The concept of fuzzy submaximal spaces is introduced and it is proved that corresponding to every fuzzy topological space, there always exists a fuzzy submaximal space which is an expansion of the given space. Fuzzy submaximal and semiregular spaces are shown to be closely associated with those spaces which are minimal or maximal with respect to certain types of properties which we call fuzzy semiregular properties. This has induced us to take up different properties for investigation whether these are fuzzy semiregular ones. Lastly we consider certain mappings between fuzzy topological spaces and study their behaviour when either or both the domain and codomain spaces are replaced by their semiregulatization spaces.