Fuzzy quasi-metric spaces

Valentín Gregori, Salvador Romaguera

Abstract

We generalize the notions of fuzzy metric by Kramosil and Michalek, and by George and Veeramani to the quasi-metric setting.We show that every quasi-metric induces a fuzzy quasi-metric and ,conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. Other basic properties are discussed.

Keywords

Fuzzy quasi-metric space; Quasi-metric; Quasi-uniformity; Bi-complete; Isometry

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Universitat Politècnica de València

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