Differentiable vector-valued functions from Euclidean space: Difference between revisions
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In the field of [[Functional Analysis]], it is possible to generalize the notion of [[derivative (mathematics)|derivative]] to infinite dimensional [[topological vector space]]s (TVSs) in multiple ways.
But when the ___domain of TVS-value functions is a subset of finite-dimensional [[Euclidean space]] then the number of generalizations of the derivative is much more limited and more well behaved.
This article presents the theory ''k''-times continuously differentiable functions on an open subset <math>\Omega</math> of Euclidean space <math>\mathbb{R}^n</math> (<math>1 \leq n < \infty</math>), which is an important special case of [[differentiation]] between arbitrary TVSs.
All vector spaces will be assumed to be over the field <math>\mathbb{F}</math>, where <math>\mathbb{F}</math> is either the [[real numbers]] <math>\mathbb{R}</math> or the [[complex numbers]] <math>\mathbb{C}</math>.
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