On some representations of functions discontinuous on countable sets

• Autorzy: Błaszczyk T. , Grande Z.
• Języki publikacji: EN

Abstrakty

EN

It is proved that every function f : R -> R having countably many of discontinuity points is the sum of two bilaterally quasi-continuous functions which are continuous at every continuity point of f.

Słowa kluczowe

EN

quasicontinuity; Darboux functions; unilateral continuity

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 3
• Strony: 543--548
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Błaszczyk T.

• Institute of Mathematics Pedagogical University Plac Weyssenhoffa 11 85-072 Bydgoszcz, Poland

autor

Grande Z.

• Institute of Mathematics Pedagogical University Plac Weyssenhoffa 11 85-072 Bydgoszcz, Poland

Bibliografia

• [1] A. M. Bruckner, Differentiation of real functions, Lectures Notes in Math. 659 (1978), Springer.
• [2] Z. Grande, On the Darboux property of the sum of cliquish functions, Real Anal. Exchange 17 (1991-92), 571-576.
• [3] A. Maliszewski, On theorems of Pu & Pu and Grande., Math. Bohemica 121 (1996), 83-87.
• [4] A. Maliszewski, Darboux Property and Quasi-Continuity. A uniform approach, Habilitation thesis, Slupsk 1996.
• [5] T. Neubrunn, Quasi-continuity, Real Anal. Exchange 14 (1988-89), 259-306.
• [6] H. W. Pu and H. H. Pu, On representations of Baire functions in a given family as sums of Baire Darboux functions with a common summand, Casopis Pest. Mat. 112 no. 3, (1987), 320-326.