On w-Isbell-convexity

Olela Otafudu, Olivier ^[2] ; Sebogodi, Katlego ^[1]
1. [1] University of Johannesburg
  
  University of Johannesburg
  
  City of Johannesburg, Sudáfrica
2. [2] School of Mathematical and Statistical Sciences North-West University, Potchefstroom Campus, Potchefstroom 2520 SOUTH AFRICA
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 1, 2022, págs. 91-105
Idioma: inglés
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Resumen
- 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.