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Locally Convex Topologies Induced by Fuzzy Norms

Author(s): Athanasios K. Katsaras

Journal: Global Journal of Mathematical Analysis
ISSN 2307-9002

Volume: 1;
Issue: 3;
Start page: 83;
Date: 2013;
Original page

It is shown that a Hausdorff topological vector space E is fuzzy normable iff its topology is a metrizable locally convex topology. Subspaces, product and quotient spaces of fuzzy normed spaces are investigated. Also the notion of the tensor product of two fuzzy normed norms is introduced and it is proved that the induced locally convex topology coincides with the projective tensor product topology.
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