Connectivity in the Higson corona of the positive real axis.

摘要

In the subject of asymptotic topology, the Higson corona of a metric space is the "part at infinity" of a certain compactification, the Higson-Roe compactification, of the metric space. The simplest nontrivial example of a Higson corona is the Higson corona of the positive real axis. Although this space is connected, it is locally disconnected. In this paper we explore the connected subsets of the space. We construct nontrivial proper closed connected subsets and give a partial classification of all such subsets of the space.