On covering properties of end and ray spaces
Combinatorics
2026-01-21 v3 General Topology
Abstract
We provide new results on combinatorial characterizations of covering properties in end spaces and ray spaces. In particular, we characterize the Lindel\"of degree, the extent, the Rothberger property, -compactness and the Menger property for ray, end and edge-end spaces. We show that -compactness and the Menger property are equivalent for these spaces, and that they are all -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.
Keywords
Cite
@article{arxiv.2510.10825,
title = {On covering properties of end and ray spaces},
author = {Rodrigo Rey Carvalho and Matheus Duzi and Vinicius de Oliveira Rodrigues},
journal= {arXiv preprint arXiv:2510.10825},
year = {2026}
}
Comments
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