Three open problems on the Wijsman topology

zbMATH Open1371.54131arXiv1609.03119MaRDI QIDQ4977474

Jiling Cao

Publication date: 16 August 2017

Abstract: Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and other hyperspace topologies, and applications of the Wijsman topology in analysis have been explored. However, there are still several fundamental open problems on this topology. In this article, the author gives a brief survey on these problems and some up-to-date partial solutions.

Full work available at URL: https://arxiv.org/abs/1609.03119

zbMATH Keywords

Wijsman topologynormalBairenon-separableWijsman hyperspacecompletely metrizablecompleteness-type properties

Mathematics Subject Classification ID

Complete metric spaces (54E50) Hyperspaces in general topology (54B20) Baire category, Baire spaces (54E52) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15)

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