Real Analysis Exchange

On Cauchy type characterizations of continuity and Baire one functions

Jacek Jachymski, Monika Lindner, and Sebastian Lindner

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In the paper of Lee et al. an equivalent condition for a function $f$ to be of the first Baire class has been established. This condition is of an $\epsilon-\delta$ type, similarly as in Cauchy's definition of continuity of a function. In the first part of this paper we examine a problem whether it is possible to obtain other classes of functions by further modifications of the above condition. It turns out that, in some sense, the answer is negative. In the second part we consider a topological version of the condition of Lee et al.

Article information

Real Anal. Exchange, Volume 30, Number 1 (2004), 339-346.

First available in Project Euclid: 27 July 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

Functions of the first Baire class continuous functions metric spaces


Jachymski, Jacek; Lindner, Monika; Lindner, Sebastian. On Cauchy type characterizations of continuity and Baire one functions. Real Anal. Exchange 30 (2004), no. 1, 339--346.

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