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A '''diffeomorphism''' is an infinitely [[derivative|differentiable]] [[homeomorphism]] with an infinitely differentiable inverse. Diffeomorphisms provide the right notion for two smooth [[manifolds]] to be "the same": if there exists a diffeomorphism, between two manifolds, then they will have all the same [[topology|topological]] properties.
A '''diffeomorphism''' is an infinitely [[derivative|differentiable]] [[homeomorphism]] with an infinitely differentiable inverse. Diffeomorphisms provide the right notion for two smooth [[manifolds]] to be "the same": if there exists a diffeomorphism, between two manifolds, then they will have all the same [[topology|topological]] properties.