Class of differentiability

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smoothness class $C^k$, $0\leq k\leq\infty, a$

A concept characterizing differentiable mappings (in particular, functions). The class $C^0$ consists of all continuous functions, the class $C^k$ consists of functions with continuous derivatives of all orders not exceeding $k$ (in particular, $C^\infty$ is the class of functions with continuous derivatives of all orders), and the class $C^a$ consists of all real-analytic functions.


The notation $C^a$ ($a$ for analytic) is somewhat unusual. Instead one mostly uses $C^\omega$ ($\omega$ denotes the first transfinite ordinal number).

How to Cite This Entry:
Class of differentiability. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article