On w-Isbell-convexity
DOI:
https://doi.org/10.4995/agt.2022.15739Keywords:
Modular pseudometric, Isbell-convexity, $w$-Isbell-convexityAbstract
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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