Remarks on asymptotic power dimension

TL;DR

This paper explores the relationship between the asymptotic power dimension of proper metric spaces and the dimension of their subpower corona, establishing conditions under which these dimensions coincide.

Contribution

It proves that, under certain conditions, the asymptotic power dimension equals the dimension of the subpower corona for proper metric spaces.

Findings

Asymptotic power dimension coincides with subpower corona dimension under specific conditions.

Provides a link between large-scale geometric properties and corona dimensions.

Utilizes a result by Dranishnikov and Smith to establish these equivalences.

Abstract

Using a result of Dranishnikov and Smith we prove that, under some conditions, the asymptotic power dimension of a proper metric space coincides with the dimension of its subpower corona.