A non-commutative approach to uniform structures

Article type: Research Article

Authors: El-Saady, Kamal^*

Affiliations: Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

Correspondence: [*] Corresponding author. Kamal El-Saady, Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt. Tel.: +201126040061; Fax: +20965211279; E-mails: [email protected] or [email protected].

Abstract: This paper presents a theory of uniform-type structures in the non-commutative sense. The theory comprises the theory of covering-uniformities for quantales as a generalization of the classical theory of covering-uniformities for frames. Also, by introducing quantale-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L a quantale). The categories of (covering) uniform quantales and L-valued uniform spaces here introduced and the adjunction between them is studied.

Keywords: Covering uniformities, uniform frames, L-quasi-topologies, quantales

DOI: 10.3233/IFS-162135

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 217-225, 2016