Concerning continuity apart from a meager set
HTML articles powered by AMS MathViewer
- by Janusz Kaniewski and Zbigniew Piotrowski PDF
- Proc. Amer. Math. Soc. 98 (1986), 324-328 Request permission
Abstract:
Given a $\sigma$-ideal $\mathcal {J}$ of subsets of a space $X$, mappings $f:X \to Y$ are investigated, such that $f|{X_0}$ is continuous for some closed ${X_0} \subset X$ with $X\backslash {X_0} \in \mathcal {J}$.References
-
S. Banach, Théorème sur les ensembles de première catégorie, Fund. Math. 16 (1930), 395-398.
- Adam Emeryk, Ryszard Frankiewicz, and Włdysław Kulpa, On functions having the Baire property, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 6, 489–491 (English, with Russian summary). MR 560185 K. Kuratowski, La propriété de Baire dans les espaces métriques, Fund. Math. 16 (1930), 390-394.
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- Kazimierz Kuratowski and Andrzej Mostowski, Set theory, Second, completely revised edition, Studies in Logic and the Foundations of Mathematics, Vol. 86, North-Holland Publishing Co., Amsterdam-New York-Oxford; PWN—Polish Scientific Publishers, Warsaw, 1976. With an introduction to descriptive set theory; Translated from the 1966 Polish original. MR 0485384
- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443 W. Sierpiński and A. Zygmund, Sur une fonction qui est discontinue sur tout ensemble de puissance du continu, Fund. Math. 4 (1923), 316-318.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 324-328
- MSC: Primary 54C30; Secondary 26A15
- DOI: https://doi.org/10.1090/S0002-9939-1986-0854041-3
- MathSciNet review: 854041