Sums of Darboux and continuous functions

• Autorzy: Juris Steprans
• Języki publikacji: EN

Abstrakty

EN

It is shown that for every Darboux function F there is a non-constant continuous function f such that F + f is still Darboux. It is shown to be consistent - the model used is iterated Sacks forcing - that for every Darboux function F there is a nowhere constant continuous function f such that F + f is still Darboux. This answers questions raised in [5] where it is shown that in various models of set theory there are universally bad Darboux functions, Darboux functions whose sum with any nowhere constant, continuous function fails to be Darboux.

Kategorie tematyczne

• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 03C55: Set-theoretic model theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994-1995
• Tom: 146
• Numer: 2
• Strony: 107-120

Daty

wydano

1995

otrzymano

1993-03-23

poprawiono

1994-02-24

Twórcy

autor

Juris Steprans

• Department of Mathematics, York University Toronto, Ontario, Canada M3J 1P3

Bibliografia

• [1] J. E. Baumgartner and R. Laver, Iterated perfect set forcing, Ann. Math. Logic 17 (1979), 271-288.
• [2] A. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659, Springer, Berlin, 1978.
• [3] A. Bruckner and J. Ceder, Darboux continuity, Jahresber. Deutsch. Math.-Verein. 67 (1965), 100.
• [4] A. Bruckner and J. Ceder, On the sums of Darboux functions, Proc. Amer. Math. Soc. 51 (1975), 97-102.
• [5] B. Kirchheim and T. Natkaniec, On universally bad Darboux functions, Real Anal. Exchange 16 (1990-91), 481-486.
• [6] P. Komjáth, A note on Darboux functions, ibid. 18 (1992-93), 249-252.
• [7] A. Miller, Mapping a set of reals onto the reals, J. Symbolic Logic 48 (1983), 575-584.
• [8] T. Radakovič, Über Darbouxsche und stetige Funktionen, Monatsh. Math. Phys. 38 (1931), 117-122.
• [9] S. Saks, Theory of the Integral, Hafner, New York, 1937.