Fuzzy quasi-metrics for the Sorgenfrey line

Authors:
ValentíN Gregori;Samuel Morillas;Bernardino Roig
Affiliations:
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain;Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain;Instituto para la Gestión Integrada de Zonas Costeras, Universidad Politécnica de Valencia, C/Paranimf 1, 46730 Gandia, Spain
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and that only one of them is right K-sequentially complete. We also observe that compatible fuzzy quasi-metrics for the Sorgenfrey line cannot be left (weakly right) K-sequentially complete.