Another word for a C^∞ (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its "functional structure" 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 four dimensions.) Milnor showed that a seven-dimensional hypersphere can be made into a smooth manifold in 28 ways.
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