ArticleOriginal scientific text
Title
Connectivity of diagonal products of Baire one functions
Authors 1
Affiliations
- Department of Mathematics, Pedagogical University, Chodkiewicza 30, 85-064 Bydgoszcz, Poland
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.
Keywords
Darboux function, peripheral continuity, approximate continuity, derivative, Baire one function, diagonal product
Bibliography
- A. M. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659, Springer, Berlin, 1978.
- A. M. Bruckner, J. Mařík and C. E. Weil, Baire one, null functions, in: Contemp. Math. 42, Amer. Math. Soc., 1985, 29-41.
- C. Goffman, C. J. Neugebauer and T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497-506.
- K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
- J. Lukeš, J. Malý and L. Zajíček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer, Berlin, 1986.
- A. Maliszewski, Characteristic functions and products of bounded derivatives, Proc. Amer. Math. Soc., to appear.
- C. J. Neugebauer, On a paper by M. Iosifescu and S. Marcus, Canad. Math. Bull. 6 (1963), 367-371.
- R. J. O'Malley, Approximately continuous functions which are continuous almost everywhere, Acta Math. Acad. Sci. Hungar. 33 (1979), 395-402.
- G. Petruska and M. Laczkovich, Baire 1 functions, approximately continuous functions and derivatives, ibid. 25 (1974), 189-212.
- Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54.
Additional information
http://matwbn.icm.edu.pl/ksiazki/fm/fm146/fm14612.pdf
Pages:
21-29
Main language of publication
English
Received
1993-03-31
Accepted
1994-03-28
Published
1994
Exact and natural sciences