Standard fuzzy uniform structures based on continuous t-norms

Authors:
J. Gutiérrez García;S. Romaguera;M. Sanchis
Affiliations:
Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain;Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain;Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

This paper deals with fuzzy uniform structures previously introduced by the authors [Fuzzy uniform structures and continuous t-norms, Fuzzy Sets Syst. 161 (2009) 1011-1021]. Our approach involves a covariant functor @J from the category of fuzzy uniform spaces and fuzzy uniformly continuous mappings (in our sense) to the category of uniform spaces and uniformly continuous mappings. We show that @J is well-behaved with respect to some significant fuzzy uniform concepts, and its behavior provides a method to introduce notions of fine fuzzy uniform structure and Stone-Cech fuzzy compactification in this context. Our method also applies to obtain fuzzy versions of some classical results on topological algebra and hyperspaces. The case of quasi-uniform structures is also analyzed.