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2004-2005 On Cauchy type characterizations of continuity and Baire one functions
Jacek Jachymski, Monika Lindner, Sebastian Lindner
Real Anal. Exchange 30(1): 339-346 (2004-2005).


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.


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Jacek Jachymski. Monika Lindner. Sebastian Lindner. "On Cauchy type characterizations of continuity and Baire one functions." Real Anal. Exchange 30 (1) 339 - 346, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 27 July 2005

zbMATH: 1071.26001
MathSciNet: MR2127539

Primary: 26A15 , 26A21

Keywords: continuous functions , Functions of the first Baire class , metric spaces

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 1 • 2004-2005
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