On convergence in the subpower Higson corona of metric spaces

TL;DR

This paper investigates the properties of the subpower Higson corona of metric spaces, showing that its closure behavior differs from the Stone-ech corona, which impacts understanding of asymptotic topology.

Contribution

It demonstrates that the closure of -compact subsets in the subpower Higson corona does not always match the Stone-ech corona, revealing new topological distinctions.

Findings

Closure of -compact sets in the subpower Higson corona can differ from the Stone-ech corona

The subpower Higson corona exhibits different convergence properties compared to the Higson corona

The results highlight nuanced differences in asymptotic topologies of metric spaces

Abstract

The subpower Higson corona of a proper metric space is defined in \cite{KZ}. We prove that, unlikely to the Higson corona, the closure of a $\sigma$-compact subset of the subpower Higson corona of a proper unbounded metric space does not necessarily coincide with its Stone-\v{C}ech corona.