On 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.