Connectivity of diagonal products of Baire one functions

Aleksander Maliszewski

Fundamenta Mathematicae (1994)

  • Volume: 146, Issue: 1, page 21-29
  • ISSN: 0016-2736

Abstract

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We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.

How to cite

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Maliszewski, Aleksander. "Connectivity of diagonal products of Baire one functions." Fundamenta Mathematicae 146.1 (1994): 21-29. <http://eudml.org/doc/212049>.

@article{Maliszewski1994,
abstract = {We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.},
author = {Maliszewski, Aleksander},
journal = {Fundamenta Mathematicae},
keywords = {Darboux function; peripheral continuity; approximate continuity; derivative; Baire one function; diagonal product; Baire one functions; connected graph},
language = {eng},
number = {1},
pages = {21-29},
title = {Connectivity of diagonal products of Baire one functions},
url = {http://eudml.org/doc/212049},
volume = {146},
year = {1994},
}

TY - JOUR
AU - Maliszewski, Aleksander
TI - Connectivity of diagonal products of Baire one functions
JO - Fundamenta Mathematicae
PY - 1994
VL - 146
IS - 1
SP - 21
EP - 29
AB - We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.
LA - eng
KW - Darboux function; peripheral continuity; approximate continuity; derivative; Baire one function; diagonal product; Baire one functions; connected graph
UR - http://eudml.org/doc/212049
ER -

References

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  1. [1] A. M. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659, Springer, Berlin, 1978. Zbl0382.26002
  2. [2] A. M. Bruckner, J. Mařík and C. E. Weil, Baire one, null functions, in: Contemp. Math. 42, Amer. Math. Soc., 1985, 29-41. Zbl0587.26004
  3. [3] C. Goffman, C. J. Neugebauer and T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497-506. Zbl0101.15502
  4. [4] K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966. 
  5. [5] J. Lukeš, J. Malý and L. Zajíček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer, Berlin, 1986. Zbl0607.31001
  6. [6] A. Maliszewski, Characteristic functions and products of bounded derivatives, Proc. Amer. Math. Soc., to appear. Zbl0833.26008
  7. [7] C. J. Neugebauer, On a paper by M. Iosifescu and S. Marcus, Canad. Math. Bull. 6 (1963), 367-371. 
  8. [8] R. J. O'Malley, Approximately continuous functions which are continuous almost everywhere, Acta Math. Acad. Sci. Hungar. 33 (1979), 395-402. Zbl0425.26001
  9. [9] G. Petruska and M. Laczkovich, Baire 1 functions, approximately continuous functions and derivatives, ibid. 25 (1974), 189-212. Zbl0279.26003
  10. [10] Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54. Zbl0038.20602

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