On Completeness of the Alexandrov Topology on a Spacetime: remarks and some corrections

TL;DR

This paper clarifies the distinction between uniform completeness and metric completeness in the context of the Alexandrov topology on spacetimes, addressing misconceptions in existing literature.

Contribution

It provides critical remarks and corrections to previous misunderstandings regarding the completeness properties of the Alexandrov topology.

Findings

Clarifies the difference between uniform and metric completeness.

Corrects misconceptions in prior studies.

Enhances understanding of spacetime topology properties.

Abstract

We clarify and discuss a misunderstanding between uniform completeness and metric completeness, that has appeared in the literature in a study on the Alexandrov topology for a spacetime.