Sublinear Higson corornae of Euclidean cones

TL;DR

This paper introduces the sublinear Higson corona concept and demonstrates its decomposition for Euclidean cones, revealing a product structure related to the base spaces and Euclidean dimensions.

Contribution

It defines the sublinear Higson corona and proves its decomposition for Euclidean cones, extending understanding of asymptotic geometric structures.

Findings

Sublinear Higson corona of Euclidean cones decomposes into product spaces.

The corona of n-dimensional Euclidean space is homeomorphic to a sphere times natural numbers.

Provides a new perspective on the asymptotic topology of Euclidean cones.

Abstract

The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional Euclidean space is homeomorphic to the product of (n-1)-dimensional sphere and that of natural numbers.