On the uniformization of lattice-valued frames

Authors:
J. Gutiérrez García;I. Mardones-Pérez;J. Picado;M. A. de Prada Vicente
Affiliations:
Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain;Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain;CMUC, Department of Mathematics, University of Coimbra, P-3001 454 Coimbra, Portugal;Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

In this note we discuss the appropriate way of uniformizing the notion of a lattice-valued frame introduced by Pultr and Rodabaugh in 2003. We cover the case of a completely distributive lattice (which is, in a certain sense, the most general one) and study the corresponding category of uniform lattice-valued frames. In particular, we show that this is a complete and cocomplete category that extends in a nice manner the category of uniform frames, widely studied in the literature.