Abstract
Let U ⊂ ℝN be any open set. A function f: U→ ℝM is said to be continuously differentiable of order k, or Ck, if / possesses all partial derivatives of order not exceeding k and all of those partial derivatives are continuous; we write f ∈ Ck or f ∈ Ck(U) if U is not clear from context. If the range of f is also not clear from context, then we write f ∈ Ck(U; ℝM). We also extend this notation to allow f ∈ C0 to indicate that f is continuous.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Krantz, S.G., Parks, H.R. (1999). Elementary Topics. In: The Geometry of Domains in Space. Birkhäuser Advanced Texts. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1574-5_1
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1574-5_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7199-4
Online ISBN: 978-1-4612-1574-5
eBook Packages: Springer Book Archive