Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

Apu Kumar Saha (Department of Mathematics, National Institute of Technology, Agartala Jirania-799055, Tripura, India)
Debasish Bhattacharya (Department of Mathematics, National Institute of Technology, Agartala Jirania-799055, Tripura, India)

Journal of Mathematical and Fundamental Sciences
Vol. 47 No. 2 (2015)

This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.