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→Definition in terms of sheaves

A '''differential manifold''' or '''smooth manifold''' is the following data:

* A [[topological ~~space~~manifold]] <math>M</math>* A subsheaf of the [[sheaf of continuous functions]] from <math>M</math> to <math>\R</math>, which plays the role of the [[sheaf of infintely differentiable functions]]~~{{fillin}}~~Such that every point has a neighbourhood with a homeomorphism to an open set in <math>\R^n</math>, such that the ring associated to that open set inthe sheaf, corresponds to the sheaf of infinitely differentiable functions on that open set.

==Relation with other structures==

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