On the insertion of Darboux functions

Aleksander Maliszewski

Fundamenta Mathematicae (1998)

  • Volume: 156, Issue: 3, page 197-209
  • ISSN: 0016-2736

Abstract

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The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.

How to cite

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Maliszewski, Aleksander. "On the insertion of Darboux functions." Fundamenta Mathematicae 156.3 (1998): 197-209. <http://eudml.org/doc/212269>.

@article{Maliszewski1998,
abstract = {The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.},
author = {Maliszewski, Aleksander},
journal = {Fundamenta Mathematicae},
keywords = {Darboux function; insertion of functions; Darboux functions},
language = {eng},
number = {3},
pages = {197-209},
title = {On the insertion of Darboux functions},
url = {http://eudml.org/doc/212269},
volume = {156},
year = {1998},
}

TY - JOUR
AU - Maliszewski, Aleksander
TI - On the insertion of Darboux functions
JO - Fundamenta Mathematicae
PY - 1998
VL - 156
IS - 3
SP - 197
EP - 209
AB - The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.
LA - eng
KW - Darboux function; insertion of functions; Darboux functions
UR - http://eudml.org/doc/212269
ER -

References

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  3. [3] J. B. Brown, Almost continuous Darboux functions and Reed's pointwise convergence criteria, Fund. Math. 86 (1974), 1-7. Zbl0297.26004
  4. [4] A. M. Bruckner, J. G. Ceder, and T. L. Pearson, On the insertion of Darboux, Baire-one functions, ibid. 80 (1973), 157-167. Zbl0271.26003
  5. [5] A. M. Bruckner, On Darboux functions, Rev. Roumaine Math. Pures Appl. 19 (1974), 977-988. Zbl0289.26005
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  9. [9] S. Kempisty, Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184-197. Zbl58.0246.01
  10. [10] A. Maliszewski, Sums of bounded Darboux functions, Real Anal. Exchange 20 (1994-95), 673-680. Zbl0830.26002
  11. [11] A. Maliszewski, On the limits of strong Świątkowski functions, Zeszyty Nauk. Politech. Łódz. Mat. 27 (1995), 87-93. Zbl0885.26002
  12. [12] A. Maliszewski, Darboux property and quasi-continuity. A uniform approach, WSP, Słupsk, 1996. 
  13. [13] T. Natkaniec, Almost continuity, Real Anal. Exchange 17 (1991-92), 462-520. 
  14. [14] T. Natkaniec, Almost continuity, WSP, Bydgoszcz, 1992. 
  15. [15] J. Stallings, Fixed point theorem for connectivity maps, Fund. Math. 47 (1959), 249-263. Zbl0114.39102
  16. [16] Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54. Zbl0038.20602

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