Regular T_0 ‐type Separations in Fuzzy Topological Spaces in the Sense of Quasi‐coincidence

Abstract

In this paper, we introduce and study three notions of property in fuzzy topological spaces using quasi-coincidence sense, and we relate to other such notions. Then, we show that all these notions satisfy good extension property. These concepts also satisfy hereditary, productive and projective properties. We note that all these concepts are preserved under one-one, onto, fuzzy regular open and fuzzy regular continuous mappings. Finally, we discuss initial and final fuzzy topological spaces on our concepts.

Keywords

• quasi‐coincidence
• regular fuzzy t_0-type separations
• fuzzy topological spaces
• initial and final fuzzy topology