Pointwise convergence topology and function spaces in fuzzy analysis

Abstract

We study the space of all continuous fuzzy-valued functions from a space $X$ into the space of fuzzy numbers $(\mathbb{E}\sp{1},d\sb{\infty})$ endowed with the pointwise convergence topology. Our results generalize the classical ones for continuous real-valued functions. The field of applications of this approach seems to be large, since the classical case allows many known devices to be fitted to general topology, functional analysis, coding theory, Boolean rings, etc.