Ball covering property and number of ends of $${\mathsf {CD}}$$ spaces with non-negative curvature outside a compact set

Abstract

In this paper, we adapt work of Z.-D. Liu to prove a ball covering property for non-branching $${\mathsf {CD}}$$ CD spaces with non-negative curvature outside a compact set. As a consequence, we obtain uniform bounds on the number of ends of such spaces.