Dept. of Mathematics, Institute of Advanced Studies, Meerut University, Meerut 250 004, India
A-26, Shastri Nagar, Meerut 250004, India
Abstract:
This paper is devoted to the study of the role of fuzzy regularly open sets. We prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings. We prove that under a fuzzy almost continuous and fuzzy almost open map, the inverse image of a fuzzy regularly open set is fuzzy regularly open. Further we define a new type of fuzzy separation axioms, fuzzy almost separation axioms. It is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology. For example, in a fuzzy almost T1 space not every fuzzy singleton is δ-closed. Also a fuzzy space which is fuzzy almost as well as fuzzy almost T0 is fuzzy almost regular. While in general topology we have to take an almost T2 space in place of almost T0 space.