A notion of weak convergence in metric spaces

TL;DR

This paper explores the concept of polar convergence in metric spaces, examining its properties, relation to Delta-convergence, potential topological structures, and applications.

Contribution

It introduces and analyzes polar convergence, connecting it with existing convergence notions and investigating its topological and applicative aspects.

Findings

Polar convergence is closely related to Delta-convergence.

Existence of a topology inducing polar convergence is investigated.

Applications of polar convergence are discussed.

Abstract

We discuss some basic properties of polar convergence in metric spaces. Polar convergence is closely connected with the notion of Delta-convergence of T.C. Lim known for several years. Possible existence of a topology which induces polar convergence is also investigated. Some applications of polar convergence follow.