Abstract
We start off with the idea of a chart. This is sometimes called a system of coordinates, but we feel, as does Lang (see [32]), that this both obscures the basic idea and impairs the recognition of an immediate generalization to Banach manifolds by introducing scads of unnecessary notation. The idea that Banach spaces provide an appropriate scenario for doing differential calculus goes back at least to the treatise [8] of Dieudonné. An extremely well-written text on smooth manifolds is Lee’s book [33].
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Sontz, S.B. (2015). Basics of Manifolds. In: Principal Bundles. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-14765-9_2
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DOI: https://doi.org/10.1007/978-3-319-14765-9_2
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