On asymptotic extension dimension

TL;DR

This paper introduces an asymptotic extension dimension concept for proper metric spaces and links it to the extension dimension of their Higson corona, enriching the understanding of large-scale geometric properties.

Contribution

It defines an asymptotic extension dimension and relates it to the extension dimension of the Higson corona, providing new insights into large-scale geometry.

Findings

Establishes a relation between asymptotic extension dimension and Higson corona extension dimension.

Introduces an asymptotic counterpart to the classical extension dimension.

Provides a framework for analyzing large-scale geometric properties of metric spaces.

Abstract

The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic extensional dimension of a proper metric space and extension dimension of its Higson corona.