Ideal closures of Busemann space and singular Minkowski space

TL;DR

This paper explores different approaches to ideal closures in Busemann nonpositively curved spaces, analyzing conditions for their equivalence and examining the structure of ideal points in singular Minkowski spaces.

Contribution

It introduces and compares two natural methods for ideal closures in Busemann spaces and studies their properties in singular Minkowski spaces.

Findings

Surjective continuation of the identity map between closures

Conditions when ideal closures coincide or differ

Description of ideal points in singular Minkowski space

Abstract

We discuss two different in general natural approaches to the ideal closure and ideal boundary of Busemann nonpositively curved metric space. It is shown that the identity map of the space admits surjective continuation from its coarse ideal closure to the weak one. We consider some situations when these closures coincide, and when they are essentially different. In particular, the singular Minkowski space is studied as flat Busemann space, and some types of its ideal points are described.