Quantale-valued Cauchy tower spaces and completeness by Gunther Jaeger and T. M. G. Ahsanullah

Journal Article
Jaeger, Gunther . 2021
Publication Work Type
Original Research Article
Magazine \ Newspaper
Journal of Applied and General Topology
Issue Number
2
Volume Number
22
Pages
461 to 481
Publication Abstract

Generalizing the concept of a probabilistic cauchy space, we introduce quantale-valued Cauchy tower  spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered  and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.

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