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Fuzzy normed linear space and its topological structure

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  • Sadeqi, I.
  • Kia, F. Solaty

Abstract

In this paper we first show that the two notations of fuzzy continuity and topological continuity are equivalent and also prove that fuzzy normed spaces are topological vector spaces; so all results in a topological vector space can be established in fuzzy normed linear space in general. Second, we introduce the notion of fuzzy seminorm and we obtain some new results. We prove that the separating family of seminorms introduces a fuzzy norm in general but it is not true in classical analysis. Finally we discuss on the application of the notion of operators between two fuzzy topological spaces, C[a,b] and R∞, for compression of images.

Suggested Citation

  • Sadeqi, I. & Kia, F. Solaty, 2009. "Fuzzy normed linear space and its topological structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2576-2589.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2576-2589
    DOI: 10.1016/j.chaos.2007.10.051
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    References listed on IDEAS

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    1. Marek-Crnjac, L., 2007. "Fuzzy Kähler manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 677-681.
    2. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
    3. El Naschie, M.S., 2006. "On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 876-881.
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    Cited by:

    1. Bînzar, Tudor & Pater, Flavius & Nădăban, Sorin, 2020. "Fuzzy bounded operators with application to Radon transform," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Sadeqi, I. & Solaty kia, F., 2009. "Some fixed point theorems in fuzzy reflexive Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2606-2612.
    3. Sorin Nădăban, 2022. "Fuzzy Continuous Mappings on Fuzzy F-Spaces," Mathematics, MDPI, vol. 10(20), pages 1-11, October.

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