Class of differentiability

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smoothness class ,

A concept characterizing differentiable mappings (in particular, functions). The class consists of all continuous functions, the class consists of functions with continuous derivatives of all orders not exceeding (in particular, is the class of functions with continuous derivatives of all orders), and the class consists of all real-analytic functions.


The notation ( for analytic) is somewhat unusual. Instead one mostly uses ( 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