Fuzzy quasi-metrics for the Sorgenfrey line

[EN] 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.1 The first and second authors acknowledge the support of Spanish Ministry of Education and Science under Grant MTM 2009-12872-C02-01.Gregori Gregori, V.; Morillas, S.; Roig, B. (2013). Fuzzy quasi-metrics for the Sorgenfrey line. Fuzzy Sets and Systems. 222:98-107. https://doi.org/10.1016/j.fss.2012.11.001S9810722