Connectivity of diagonal products of Baire one functions
Maliszewski, Aleksander
Fundamenta Mathematicae, Tome 144 (1994), p. 21-29 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:212049
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     author = {Aleksander Maliszewski},
     title = {Connectivity of diagonal products of Baire one functions},
     journal = {Fundamenta Mathematicae},
     volume = {144},
     year = {1994},
     pages = {21-29},
     zbl = {0823.26002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv146i1p21bwm}
}
Maliszewski, Aleksander. Connectivity of diagonal products of Baire one functions. Fundamenta Mathematicae, Tome 144 (1994) pp. 21-29. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i1p21bwm/

[00000] [1] A. M. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659, Springer, Berlin, 1978. | Zbl 0382.26002

[00001] [2] A. M. Bruckner, J. Mařík and C. E. Weil, Baire one, null functions, in: Contemp. Math. 42, Amer. Math. Soc., 1985, 29-41. | Zbl 0587.26004

[00002] [3] C. Goffman, C. J. Neugebauer and T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497-506. | Zbl 0101.15502

[00003] [4] K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.

[00004] [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. | Zbl 0607.31001

[00005] [6] A. Maliszewski, Characteristic functions and products of bounded derivatives, Proc. Amer. Math. Soc., to appear. | Zbl 0833.26008

[00006] [7] C. J. Neugebauer, On a paper by M. Iosifescu and S. Marcus, Canad. Math. Bull. 6 (1963), 367-371.

[00007] [8] R. J. O'Malley, Approximately continuous functions which are continuous almost everywhere, Acta Math. Acad. Sci. Hungar. 33 (1979), 395-402. | Zbl 0425.26001

[00008] [9] G. Petruska and M. Laczkovich, Baire 1 functions, approximately continuous functions and derivatives, ibid. 25 (1974), 189-212. | Zbl 0279.26003

[00009] [10] Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54. | Zbl 0038.20602