Quantale-valued Cauchy tower spaces and completeness


  • Gunther Jäger University of Applied Sciences Stralsund
  • T. M. G. Ahsanullah King Saud University




Cauchy space, quantale-valued metric space, quantale-valued uniform convergence tower space, completeness, completion, Cauchy completeness


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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Author Biographies

Gunther Jäger, University of Applied Sciences Stralsund

School of Mechanical Engineering

T. M. G. Ahsanullah, King Saud University

Department of Mathematics,College of Science


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How to Cite

G. Jäger and T. M. G. Ahsanullah, “Quantale-valued Cauchy tower spaces and completeness”, Appl. Gen. Topol., vol. 22, no. 2, pp. 461–481, Oct. 2021.