Open AccessMathematics

Fuzzy quasi-metric spaces

V. Gregori, S. Romaguera

2004.4.1Applied General Topology

DOI: 10.4995/agt.2004.2001

tlooto Summary

It is shown that every quasi-metric induces a fuzzy quasi-Metric space and, conversely, every fuzzy semi-metrizable space generates a quasi- metrizable topology.

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.

Citation format

GREGORI, V.; ROMAGUERA, S. Fuzzy quasi-metric spaces. Applied General Topology, 2004, 5: 129–136.