Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Sets of points of discontinuity
HTML articles powered by AMS MathViewer

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

Abstract:

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.
References
    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.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C30, 26A15
  • Retrieve articles in all journals with MSC: 54C30, 26A15
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 38 (1973), 193-197
  • MSC: Primary 54C30; Secondary 26A15
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0312457-9
  • MathSciNet review: 0312457