The Alexander horned sphere is a pathological object in topology discovered by J. W. Alexander (1924). It is a particular topological embedding of a two-dimensional sphere in three-dimensional space. Together with its inside, it is a topological 3-ball, the Alexander horned ball, and so is simply connected; i.e., every loop can be shrunk to a point while staying inside. However, the exterior is not simply connected, unlike the exterior of the usual round sphere.