On lattice-valued frames: The completely distributive case

Authors:
Javier Gutiérrez García;Ulrich Höhle;María Angeles de Prada Vicente
Affiliations:
Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain;Fachbereich C Mathematik und Naturwissenschaften, Bergische Universität, D-42097 Wuppertal, Germany;Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain
Venue:
Fuzzy Sets and Systems
Year:
2010

Citing 3
Cited 4

Category theoretic aspects of chain-valued frames: Part I: Categorical and presheaf theoretic foundations

Fuzzy Sets and Systems
Category theoretic aspects of chain-valued frames: Part II: Applications to lattice-valued topology

Fuzzy Sets and Systems
Uniform-type structures on lattice-valued spaces and frames

Fuzzy Sets and Systems

An approach to fuzzy frames via fuzzy posets

Fuzzy Sets and Systems
On the uniformization of lattice-valued frames

Fuzzy Sets and Systems
A survey of fuzzifications of frames, the Papert--Papert--Isbell adjunction and sobriety

Fuzzy Sets and Systems
Sobriety and spatiality in categories of lattice-valued algebras

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.20

Visualization

Abstract

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501-528 and 529-558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a completely distributive lattice. In particular, L-Frm is complete and cocomplete. Finally we prove that, in a certain sense, the assumption of L being a completely distributive lattice cannot be weakened.