Locally Convex Topologies Induced by Fuzzy Norms

  • Authors

    • Athanasios K. Katsaras Department of Mathematics, University of Ioannina, Greece
    https://doi.org/10.14419/gjma.v1i3.1046

    Received date: June 6, 2013

    Accepted date: June 6, 2013

    Published date: June 15, 2013

  • Abstract

    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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  • How to Cite

    Katsaras, A. K. (2013). Locally Convex Topologies Induced by Fuzzy Norms. Global Journal of Mathematical Analysis, 1(3), 83-96. https://doi.org/10.14419/gjma.v1i3.1046