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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sets of points of discontinuity
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by Richard Bolstein PDF
Proc. Amer. Math. Soc. 38 (1973), 193-197 Request permission


In order that a subset $F$ of a topological space coincide with the set of points of discontinuity of a real-valued function on the space, it is necessary that $F$ be an ${F_\sigma }$-set devoid of isolated points. It is shown that this condition is also sufficient if the space is β€œalmost-resolvable", and in particular if the space is either separable, first countable, locally compact Hausdorff, or topological linear.
    H. Hahn, Reelle Funktionen, Akademie Verlagsgesellschaft, Leipzig, 1932; reprint, Chelsea, New York, 1948.
  • Edwin Hewitt, A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309–333. MR 8692
  • Edwin Hewitt and Karl Stromberg, Real and abstract analysis. A modern treatment of the theory of functions of a real variable, Springer-Verlag, New York, 1965. MR 0188387
  • W. H. Young, Über die Einteilung der unstetigen Funtionen und die Verteilung ihrer Stetigkeitspunkte, S.-B. Akad. Wiss. Wien Math.-Natur. K. Abt. IIA 112 (1907), 1307-1311.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 38 (1973), 193-197
  • MSC: Primary 54C30; Secondary 26A15
  • DOI:
  • MathSciNet review: 0312457