On w-Isbell-convexity





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


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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How to Cite

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