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DiffeomorphismGiven two differentiable manifolds M and N (they could be the same), a bijective map f from M to N is called a diffeomorphism if there is an open cover of M by compatible coordinate charts such that {f(U):U is a chart of M} is an open cover of N by compatible charts with smooth compatibility conditions.To put it another way, a diffeomorphism is a bijective smooth map. It also happens to be a homeomorphism. This article is a stub. You can help Wikipedia by fixing it. 
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Diffeomorphism".