Abstract:

The definitions of fuzzy open ball and fuzzy closed ball are introduced and some properties of them are proved. Then fuzzy open and fuzzy closed sets are defined which can induced a topology on a generalized fuzzy normed space (X,N,*). Finally two conclusions of a complete generalized fuzzy normed space are proved by the concept of nest of fuzzy closed balls in a generalized fuzzy normed space.

Key words: generalized fuzzy normed space; fuzzy convergence; fuzzy boundedness; nest of fuzzy closed balls