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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 326417, 11 pages
http://dx.doi.org/10.1155/2012/326417
Research Article

On the Fuzzy Number Space with the Level Convergence Topology

Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain

Received 11 October 2012; Accepted 7 November 2012

Academic Editor: Salvador Romaguera

Copyright © 2012 J. J. Font et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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