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Nonstandard analysis and differentiable manifolds - Foundations

By R Almeida


We approach the study of di erentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the category of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations for the tangent bundle, di erentiable function, di erential of a function, directional derivatives, etc. We establish some relations between our de nitions and the classical ones.CEOCFCTFEDER/POCI 201

Topics: Nonstandard analysis, differentiable manifolds, tangent bundle, infinitesimal transformation
Publisher: Balkan Society of Geometers
Year: 2009
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