The Hahn-Banach extension theorem for fuzzy normed spaces revisited
Summary: This paper deals with fuzzy normed spaces in the sense of \textit{S.-C. Cheng} and \textit{J. N. Mordeson} [Bull. Calcutta Math. Soc. 86, No. 5, 429--436 (1994; Zbl 0829.47063)]. 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.
scientific article; zbMATH DE number 7021816