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Separation of fuzzy normed linear spaces. (English) Zbl 0849.46058
Summary: This paper deals with Hausdorff separation axiom for fuzzy topological spaces. The necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated. Properties of separated and non-separated fuzzy norms along with examples are studied. Separation of a fuzzy norm in terms of the ordinary norm it induces and its consequences are characterized. Separation of quotient fuzzy semi-norm is studied.

46S40Fuzzy functional analysis
46A22Theorems of Hahn-Banach type; extension and lifting of functionals and operators
Full Text: DOI
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[2] Katsaras, A. K.: Fuzzy topological vector spaces I. Fuzzy sets and systems 6, 85-95 (1981) · Zbl 0463.46009
[3] Katsaras, A. K.: Fuzzy topological vector spaces II. Fuzzy sets and systems 12, 143-154 (1984) · Zbl 0555.46006
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[6] Sarma, K. K. M.: Fuzzy normed linear spaces. Doctoral dissertation (1990)