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On the L-fuzzy topological spaces

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  • Saadati, Reza

Abstract

As a natural generalization of fuzzy metric spaces due to George and Veeramani [George A, Veeramani P. On some result in fuzzy metric space. Fuzzy Sets Syst 1994;64:395–9], the present author defined the notion of L-fuzzy metric spaces. In this paper we prove some known results of metric spaces including Uniform continuity theorem and Ascoli–Arzela theorem for L-fuzzy metric spaces. We also prove that every L-fuzzy metric space has a countably locally finite basis and use this result to conclude that every L-fuzzy metric space is metrizable.

Suggested Citation

  • Saadati, Reza, 2008. "On the L-fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1419-1426.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:5:p:1419-1426
    DOI: 10.1016/j.chaos.2006.10.033
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    References listed on IDEAS

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    1. El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    2. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    3. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
    4. Gregori, V. & Romaguera, S. & Veeramani, P., 2006. "A note on intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 902-905.
    5. Saadati, Reza & Razani, Abdolrahman & Adibi, H., 2007. "A common fixed point theorem in L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 358-363.
    6. 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. Masoumeh Madadi & Donal O’Regan & Choonkil Park & Manuel de la Sen & Reza Saadati, 2020. "On the Topology Induced by C *-Algebra-Valued Fuzzy Metric Spaces," Mathematics, MDPI, vol. 8(6), pages 1-10, June.

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