On the sum of Darboux functions
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- by A. M. Bruckner and J. Ceder
- Proc. Amer. Math. Soc. 51 (1975), 97-102
- DOI: https://doi.org/10.1090/S0002-9939-1975-0387507-6
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Abstract:
The main purpose is to indicate how badly the sum of a continuous function with a Darboux function can fail to be a Darboux function.References
- A. M. Bruckner and J. G. Ceder, Darboux continuity, Jber. Deutsch. Math.-Verein. 67 (1964/65), no. Abt. 1, 93–117. MR 186761
- A. M. Bruckner, J. G. Ceder, and R. Keston, Representations and approximations by Darboux functions in the first class of Baire, Rev. Roumaine Math. Pures Appl. 13 (1968), 1246–1254. MR 243008
- A. M. Bruckner, J. G. Ceder, and Max Weiss, Uniform limits of Darboux functions, Colloq. Math. 15 (1966), 65–77. MR 197629, DOI 10.4064/cm-15-1-65-77
- H. Fast, Une remarque sur la propriété de Weierstrass, Colloq. Math. 7 (1959), 75–77 (French). MR 120332, DOI 10.4064/cm-7-1-75-77
- A. B. Gurevič, $D$-continuous Sierpiński components, Dokl. Akad. Nauk BSSR 10 (1966), 539–541 (Russian). MR 0204585
- Ladislav Mišík, Zu zwei Sätzen von W. Sierpinski, Rev. Roumaine Math. Pures Appl. 12 (1967), 849–860 (German). MR 223509
- Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578
- W. Sierpiński, Sur une propriété de fonctions réelles quelconques, Matematiche (Catania) 8 (1953), no. 2, 43–48 (French). MR 64125
- Rudolf Švarc, On the range of values of the sum of a continuous and a Darboux function, Časopis Pěst. Mat. 98 (1973), 178–180, 213 (English, with Czech summary). MR 0322106
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 51 (1975), 97-102
- MSC: Primary 26A15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0387507-6
- MathSciNet review: 0387507