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Smooth Manifold

Another word for a $C^\infty$ (infinitely differentiable) Manifold. A smooth manifold is a Topological Manifold together with its ``functional structure'' (Bredon 1995) and so differs from a Topological Manifold because the notion of differentiability exists on it. Every smooth manifold is a Topological Manifold, but not necessarily vice versa. (The first nonsmooth Topological Manifold occurs in 4-D.) In 1959, Milnor showed that a 7-D Hypersphere can be made into a smooth manifold in 28 ways.

See also Differentiable Manifold, Hypersphere, Manifold, Topological Manifold


Bredon, G. E. Topology & Geometry. New York: Springer-Verlag, p. 69, 1995.

© 1996-9 Eric W. Weisstein