Uniform convergence of distance functionals under remetrization and infima of hyperspace topologies
Year: 2026
Type: article
Abstract: The objective of this article is twofold. In the first half of the article, we investigate upper parts of the hyperspace convergences determined by uniform convergence of distance functionals on a bornology under different metrizations of a metrizable space. To do this, a new covering property associated with the underlying bornology is introduced. An independent study of this new covering notion in relation to some well-known notions, such as strong uniform continuity, is also presented. In the second half, we study the infima of hyperspace convergences (induced by distance functionals) determined by a family of (uniformly) equivalent metrics. In particular, we establish the existence of the minimum element for the collection of upper Attouch–Wets convergences corresponding to all equivalent metrics on a metrizable space X . We show that such a minimum element exists if and only if X has a compatible Heine–Borel metric. Our findings give several new insights into the theory of hyperspace convergences.
Source: Canadian Journal of Mathematics
Authors: Yogesh Agarwal, Varun Jindal
Institution: Malaviya National Institute of Technology Jaipur
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7128798848
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