On w-Isbell-convexity

Authors

DOI:

https://doi.org/10.4995/agt.2022.15739

Keywords:

Modular pseudometric, Isbell-convexity, $w$-Isbell-convexity

Abstract

Chistyakov introduced and developed a concept of modular metric for an arbitrary set in order to generalise the classical notion of modular on a linear space. In this article, we introduce the theory of hyperconvexity in the setting of modular pseudometric that is herein called w-Isbell-convexity. We show that on a modular set, w-Isbell-convexity is equivalent to hyperconvexity whenever the modular pseudometric is continuous from the right on the set of positive numbers.

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Author Biographies

Olivier Olela Otafudu, North-West University

School of Mathematical and Statistical Sciences

Katlego Sebogodi, University of Johannesburg

Department of Mathematics and Applied Mathematics

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Published

2022-04-01

How to Cite

[1]
O. Olela Otafudu and K. Sebogodi, “On w-Isbell-convexity”, Appl. Gen. Topol., vol. 23, no. 1, pp. 91–105, Apr. 2022.

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