Sets of points of discontinuity
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- 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 βalmost-resolvable", and in particular if the space is either separable, first countable, locally compact Hausdorff, or topological linear.References
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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), 309β333. 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, Γber die Einteilung der unstetigen Funtionen und die Verteilung ihrer Stetigkeitspunkte, S.-B. Akad. Wiss. Wien Math.-Natur. K. Abt. IIA 112 (1907), 1307-1311.
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