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An equivalent definition of functions of the first Baire class

Author(s): Peng-Yee Lee; Wee-Kee Tang; Dongsheng Zhao
Journal: Proc. Amer. Math. Soc. 129 (2001), 2273-2275.
MSC (2000): Primary 26A21
Posted: November 30, 2000
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Abstract: An equivalent definition of functions of the first Baire class in terms of $\varepsilon-\delta$ is given.

References:

[1]: Baire, R., Sur les fonctions des variables réeles, Ann. Mat. Pura ed Appl. 3(1899), 1-122.
[2]: Kuratowski, K., Topology, Academic Press, London, 1966. MR 36:840
[3]: Natanson, I. P., Theory of functions of a real variable, Vol. 2, Frederick Ungar Publishing Co., New York, 1961. MR 26:6309

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Additional Information:

Peng-Yee Lee
Affiliation: Division of Mathematics, National Institute of Education, Nanyang Technological University, 469, Bukit Timah Road, Singapore 259756
Email: pylee@nie.edu.sg

Wee-Kee Tang
Affiliation: Division of Mathematics, National Institute of Education, Nanyang Technological University, 469, Bukit Timah Road, Singapore 259756
Email: wktang@nie.edu.sg

Dongsheng Zhao
Affiliation: Division of Mathematics, National Institute of Education, Nanyang Technological University, 469, Bukit Timah Road, Singapore 259756
Email: dszhao@nie.edu.sg

DOI: 10.1090/S0002-9939-00-05826-3
PII: S 0002-9939(00)05826-3
Keywords: Functions of the first Baire class, continuity, metric spaces
Received by editor(s): June 2, 1999
Received by editor(s) in revised form: November 18, 1999
Posted: November 30, 2000
Additional Notes: We thank A. B. Aruffo, L. Zajicek and the referee for their comments contributing to the current proof and final statement of Theorem 1.
Communicated by: David Preiss
Copyright of article: Copyright 2000, American Mathematical Society


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