Sierpinski objects in subcategories of FTS

Abstract

E.G. Manes gave a characterization of the category of topological spaces as a suitable category of sets with structure having an appropriate “Sierpinski object”. By identifying an appropriate Sierpinski object, A.K. Srivastava and R. Srivastava obtained an analogous characterization of the category of fuzzy topological spaces. In the present paper, we extend these ideas further and give similar characterizations of the categories of fuzzy neighbourhood spaces and topological fuzzy topological spaces by identifying appropriate Sierpinski objects in these categories. AHS Subject Classifications : 54A40. 54B30, 18R30. 18B99, 18A40. © 1988 Taylor & Francis Group, LLC.