
Journal of Convex Analysis 29 (2022), No. 3, 717730 Copyright Heldermann Verlag 2022 Metrization of Idempotent Convex Compacta Oleh Nykyforchyn Institute of Mathematics, Casimir the Great University, Bydgoszcz, Poland and: Dept. of Mathematics and Computer Science, V. Stefanyk Precarpathian National University, IvanoFrankivsk, Ukraine oleh.nyk@gmail.com Mariia Savchyn Dept. of Mathematics and Computer Science, V. Stefanyk Precarpathian National University, IvanoFrankivsk, Ukraine savchyn.mar@gmail.com [Abstractpdf] Using a convenient subbase on the second hyperspace of a compactum with the Vietoris topology, we prove that the mapping that takes each closed nonempty subset $A$ of an $I$convex compactum $X$ to its closed idempotent convex hull is continuous. This implies that each neighborhood of the diagonal $\Delta_X\subset X\times X$ contains an idempotent convex neighborhood. The main result is the theorem that the topology on an idempotent convex compactum $X$ is determined by a family of idempotent convex pseudometrics (with one idempotent convex metric if $X$ is metrizable). Keywords: Iconvex compactum, idempotent semimodule, locally convex space, Vietoris topology, metrization MSC: 52A01, 52A30, 15A80, 46S99. [ Fulltextpdf (138 KB)] for subscribers only. 