On the L-fuzzy topological spaces

Reza Saadati

Chaos, Solitons & Fractals, 2008, vol. 37, issue 5, 1419-1426

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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:37:y:2008:i:5:p:1419-1426

DOI: 10.1016/j.chaos.2006.10.033

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