In the proof of theorem 5.2 of Spivak's calculus on manifolds, he invokes the inverse function theorem for a function g that he defines there without ever assuming that it was continuously differentiable. Is this a typo?
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The function $g$ is defined as $$g(a,b)=f(a)+(0,b)$$ with $f$...
Martín-Blas Pérez Pinilla
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f is a coordinate system which he assumes to be differentiable but not continuously differentiable – user68432 May 30 '14 at 08:45
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3At least part way through Spivak, the author states that he will henceforth use "differentiable" to mean "infinitely differentiable". – Christopher A. Wong May 30 '14 at 08:58
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1@user68432, see the first paragraph of Ch. 5. – Martín-Blas Pérez Pinilla May 30 '14 at 09:00
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Ok, thanks Christopher. And you too Martin! – user68432 May 30 '14 at 09:00