On the fuzzy number space with the level convergence topology

Abstract

We characterize compact sets of 1 endowed with the level convergence topology τℓ. We also describe the completion (1 ̂, ̂) of 1 with respect to its natural uniformity, that is, the pointwise uniformity and show other topological properties of 1 ̂, as separability. We apply these results to give an Arzela-Ascoli theorem for the space of (1, τℓ) -valued continuous functions on a locally compact topological space equipped with the compact-open topology. Copyright © 2012 J. J. Font et al.