Lee, Peng-Yee; Tang, Wee-Kee; Zhao, Dongsheng An equivalent definition of functions of the first Baire class. (English) Zbl 0970.26004 Proc. Am. Math. Soc. 129, No. 8, 2273-2275 (2001). Let \(f:X \to Y\) be a mapping between complete separable metric spaces \((X,d_X)\) and \((Y,d_Y)\). Then \(f\) is of the first Baire class if and only if for each \(r > 0\) there is a function \(\eta > 0\) on \(X\) such that \(d_Y(f(x),f(y)) < r\) whenever \(d_X(x,y) < \min(\eta (x),\eta (y))\). Reviewer: Zbigniew Grande (Bydgoszcz) Cited in 6 ReviewsCited in 5 Documents MSC: 26A21 Classification of real functions; Baire classification of sets and functions 54E50 Complete metric spaces 54C08 Weak and generalized continuity 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable Keywords:complete separable metric spaces; Baire 1 mapping; continuity PDF BibTeX XML Cite \textit{P.-Y. Lee} et al., Proc. Am. Math. Soc. 129, No. 8, 2273--2275 (2001; Zbl 0970.26004) Full Text: DOI References: [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. · Zbl 0158.40901 [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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.