The bicompletion of fuzzy quasi-metric spaces

Authors:
F. Castro-Company;S. Romaguera;P. Tirado
Affiliations:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain;Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain;Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced by its bicompletion.