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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.

MSC:

46S40 Fuzzy functional analysis
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
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References:

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