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Abstract and Applied Analysis
Volume 2014, Article ID 151472, 7 pages
http://dx.doi.org/10.1155/2014/151472
Research Article

The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited

Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 Valencia, Spain

Received 13 March 2014; Accepted 13 May 2014; Published 28 May 2014

Academic Editor: Manuel Sanchis

Copyright © 2014 Carmen Alegre and Salvador Romaguera. 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

This paper deals with fuzzy normed spaces in the sense of Cheng and Mordeson. We characterize fuzzy norms in terms of ascending and separating families of seminorms and prove an extension theorem for continuous linear functionals on a fuzzy normed space. Our result generalizes the classical Hahn-Banach extension theorem for normed spaces.