An alternative way of characterizing an n-manifold is as an object that can locally be described by n real coordinates. That is, any sufficiently small neighborhood is homeomorphic to an open set in t...An alternative way of characterizing an n-manifold is as an object that can locally be described by n real coordinates. That is, any sufficiently small neighborhood is homeomorphic to an open set in the space of real-valued n-tuples of the form (x1, x2, . . . , xn). For example, a closed half-plane is not a 2-manifold because no neighborhood of a point on its edge is homeomorphic to any open set in the Cartesian plane.
