Three open problems on the Wijsman topology

TL;DR

This paper surveys three fundamental open problems related to the Wijsman topology, highlighting their significance, recent partial solutions, and the ongoing research challenges in understanding this topology's properties and applications.

Contribution

It identifies and discusses three key open problems in the study of the Wijsman topology, providing a concise overview and recent partial solutions.

Findings

Identification of three open problems in Wijsman topology

Recent partial solutions to some of these problems

Highlighting the importance of these problems in topology and analysis

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.