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Differentiable manifold Smooth Manifold from Wolfram MathWorld A smooth manifold is a topological manifold together with its functional structure Bredon and so differs from a topological manifold because the notion of differentiability exists on it Every smooth manifold Introduction to Smooth Manifolds Graduate Texts in Mircea Craioveanu, Zentralblatt MATH, Vol , This text provides an elementary introduction to smooth manifolds which can be understood by junior undergraduates There are Smooth manifolds Universiteit Utrecht SMOOTH MANIFOLDS Definition . An m dimensional smooth structure on a topological space M is an m dimensional smooth atlas A on M which is maximal, i.e with the property that there is no smooth What is a smooth manifold anyway Simplicial Thoughts Oct , Intuitively, a smooth manifold is a space that locally looks like some Euclidean space Thus we can carry out all the usual nice mathematical things we look to do, find limits of sequences, do calculus, etc, etc So smooth manifolds INTRODUCTION TO SMOOTH MANIFOLDS Higher Intellect ory, embeddings of smooth manifolds into Euclidean spaces, approximation of continuous maps by smooth ones, and quotients of manifolds by group actions.