Open Alexandrov spaces of nonnegative curvature

Let [Formula: see text] be an open (i.e. complete, non-compact and without boundary) Alexandrov [Formula: see text]-space of nonnegative curvature with a soul [Formula: see text]. In this paper, we will establish several structural results on [Formula: see text] that can be viewed as counterparts of structural results on an open Riemannian manifold with nonnegative sectional curvature.