Alexandrov spaces with nonnegative curvature out-side a compact set (Q1382661)

An Alexandrov space with curvature bounded below is a length space such that the Alexandrov-Topogonov comparison theorem holds for all small geodesic triangles. As an extension of Riemannian geometry, any complete noncompact Alexandrov space \((X, \circ)\) of finite Hausdorff dimension, with base point \(\circ\) and non-negative curvature outside the geodesic ball \(B(\circ,a)\) centred in \(\circ\) of radius \(a\), has the number of ends uniformly bounded above. If a is small enough, then the space has at most two ends.