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Jäger, Gunther; Ahsanullah, T. M. G.

Quantale-valued Cauchy tower spaces and completeness. (English) Zbl 1508.54016

Appl. Gen. Topol. 22, No. 2, 461-481 (2021).
The authors generalize the concept of a probabilistic Cauchy space introduced by G. D. Richardson and D. C. Kent [J. Aust. Math. Soc., Ser. A 61, No. 3, 400–420 (1996; Zbl 0943.54002)] to quantale-valued Cauchy tower spaces. They also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.
Reviewer: Javier Gutiérrez García (Bilbao)

MSC:

54E70 Probabilistic metric spaces
18F75 Quantales
06F07 Quantales
54E15 Uniform structures and generalizations
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)

Keywords:

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

Citations:

Zbl 0943.54002
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Full Text: DOI
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References:

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