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Transactions of the American Mathematical Society

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A generalization of a theorem of Maximoff and applications


Author: S. J. Agronsky
Journal: Trans. Amer. Math. Soc. 273 (1982), 767-779
MSC: Primary 26A21; Secondary 26A24
DOI: https://doi.org/10.1090/S0002-9947-1982-0667173-0
MathSciNet review: 667173
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Abstract: Many classes of functions can be characterized in terms of their associated sets. Maximoff gave another type of characterization for the approximately continuous functions. In this paper, we give the conditions under which the two types of characterizations are equivalent. We then show that many classes of functions defined or characterized in terms of their associated sets also admit Maximoff-type characterizations.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0667173-0
Keywords: Zahorski's $ {\mathfrak{M}_1}$ classes, Darboux-Baire $ 1$ functions
Article copyright: © Copyright 1982 American Mathematical Society

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