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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An equivalent definition of functions of the first Baire class


Authors: Peng-Yee Lee, Wee-Kee Tang and Dongsheng Zhao
Journal: Proc. Amer. Math. Soc. 129 (2001), 2273-2275
MSC (2000): Primary 26A21
Published electronically: November 30, 2000
MathSciNet review: 1823909
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Abstract | References | Similar Articles | Additional Information

Abstract: An equivalent definition of functions of the first Baire class in terms of $\varepsilon-\delta$ is given.


References [Enhancements On Off] (What's this?)

  • [1] Baire, R., Sur les fonctions des variables réeles, Ann. Mat. Pura ed Appl. 3(1899), 1-122.
  • [2] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751 (36 #840)
  • [3] I. P. Natanson, Theory of functions of a real variable. Vol. II, Translated from the Russian by Leo F. Boron, Frederick Ungar Publishing Co., New York, 1961. MR 0148805 (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: http://dx.doi.org/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
Published electronically: November 30, 2000
Additional Notes: We thank A. B. Aruffo, L. Zajiček and the referee for their comments contributing to the current proof and final statement of Theorem 1.
Communicated by: David Preiss
Article copyright: © Copyright 2000 American Mathematical Society



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