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 T 1 space not every fuzzy singleton is δ-closed. Also a fuzzy space which is fuzzy almost T 2 1 2 as well as fuzzy almost T 0 is fuzzy almost regular. While in general topology we have to take an almost T 2 space in place of almost T 0 space.
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