ON LEBESGUE PROPERTY FOR FUZZY METRIC SPACES

ON LEBESGUE PROPERTY FOR FUZZY METRIC SPACES

Sugata Adhya, A. Deb Ray

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Abstract

We provide several characterizations of the Lebesgue property for fuzzy metric spaces. It is known that a fuzzy metric space is Lebesgue if and only if every real-valued continuous function is uniformly continuous. Here we show that it suces to examine uniform continuity of bounded real-valued continuous functions for characteriz- ing Lebesgue property in fuzzy setting.

Keywords

Fuzzy metric space, uniformly continuous function, Lebesgue property.