On the Fuzzy Number Space with the Level Convergence Topology. (6th December 2012) - Font, J. J.; Miralles, A.; Sanchis, M.
Abstract : We characterize compact sets of 𝔼 1 endowed with the level convergence topology τ ℓ . We also describe the completion ( 𝔼 1 ̂, 𝒰 ̂ ) of 𝔼 1 with respect to its natural uniformity, that is, the pointwise uniformity 𝒰, and show other topological properties of 𝔼 1 ̂, as separability. We apply these results to give an Arzela-Ascoli theorem for the space of ( 𝔼 1, τ ℓ ) -valued continuous functions on a locally compact topological space equipped with the compact-open topology.