Generalized Closed Sets in Fuzzy Topological Spaces and Their Properties

Author(s)	Abhijit Aryan, Dr. K.N. Jha
Country	India
Abstract	In this paper, we introduce and study the concept of generalized closed sets in fuzzy topological spaces. We define various types of generalized closed sets, including fuzzy generalized closed sets, fuzzy semi-generalized closed sets, and fuzzy weakly generalized closed sets, and investigate their fundamental properties. Relationships among these classes of sets are established, and several characterizations are provided. We also examine the behavior of these sets under fuzzy continuous mappings and fuzzy homeomorphisms. Furthermore, some new separation axioms based on generalized closed sets in fuzzy topological spaces are introduced, and their interrelations are discussed. Illustrative examples are given to support the results and to show the distinctions between the different classes of sets.
Keywords	Fuzzy topological space; Generalized closed set; Fuzzy generalized closed set; Fuzzy homeomorphism and Weakly generalized closed set etc.
Published In	Volume 8, Issue 3, May-June 2026
Published On	2026-06-01
DOI	https://doi.org/10.36948/ijfmr.2026.v08i03.85644

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