# Class of differentiability

From Encyclopedia of Mathematics

*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.

#### Comments

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: http://encyclopediaofmath.org/index.php?title=Class_of_differentiability&oldid=31846

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article