On covering properties of end and ray spaces

Abstract

We provide new results on combinatorial characterizations of covering properties in end spaces and ray spaces. In particular, we characterize the Lindelöf degree, the extent, the Rothberger property, $\sigma$-compactness and the Menger property for ray, end and edge-end spaces. We show that $\sigma$-compactness and the Menger property are equivalent for these spaces, and that they are all $D$-spaces. As an application of some of these characterizations, we are able to provide combinatorial characterizations of graphs with countably many ends and edge-ends.

A few new results, including a combinatorial chracterization of graphs with countably many ends and edge and/or edge-ends. The introduction now presents a list of the main results of this paper