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** An automorphism of a differentiable manifold M is a diffeomorphism from M to itself.
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** and automorphism
** In the category of Riemann surfaces, an automorphism is a bijective biholomorphic map ( also called a conformal map ), from a surface to itself.
** In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism ( see homeomorphism group ).
** and differentiable
** Conversely, if ƒ: I → R is absolutely continuous and thus differentiable almost everywhere, and satisfies | ƒ ′( x )| ≤ K for almost all x in I, then ƒ is Lipschitz continuous with Lipschitz constant at most K.
** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.
** Reciprocity relation or exact differential, a mathematical differential of the form dQ, for some differentiable function Q
** Differential topology, in multivariable calculus, the differential of a smooth map between Euclidean spaces or differentiable manifolds is the approximating linear map between the tangent spaces, called pushforward ( differential )
** and manifold
** Lorentz surface, a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics.
** The representation's material (' Stoff ') is a given or received manifold of sensation which is unified when it is attributed to a transcendental object.
** 1995-1997 Honda Accord, For this particular vehicle the engine was updated with a more efficient intake manifold.
** Exotic R < sup > 4 </ sup >-differentiable manifold homeomorphic but not diffeomorphic to the Euclidean space R < sup > 4 </ sup >
** and M
David Pears and Brian McGuinness ( 1961 ), Routledge, hardcover: ISBN 0-7100-3004-5, 1974 paperback: ISBN 0-415-02825-6, 2001 hardcover: ISBN 0-415-25562-7, 2001 paperback: ISBN 0-415-25408-6 ; ** Philosophische Untersuchungen ( 1953 ) or Philosophical Investigations, translated by G. E. M.
** M. C. Escher used special shapes of mirrors in order to achieve a much more complete view of his surroundings than by direct observation in Hand with Reflecting Sphere ( also known as Self-Portrait in Spherical Mirror ).
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