Maximal classes for the family of quasi-continuous functions with closed graph

• Autorzy: Sieg W.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider classes of functions f : R - R. The maximal additive class for the family QU of quasi-continuous functions with closed graph is equal to the class of all continuous functions. We also show that the maximal multiplicative class for QU is equal to a class of continuous functions, which fulfil an extra condition.

Słowa kluczowe

EN

continuous functions; closed graph

PL

funkcje ciągłe; graf zamknięty

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 1
• Strony: 41--45
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Sieg W.

• Casimirus the Great University Department of Mathematics Plac Weyssenhoffa 11 85-072 Bydgoszcz, Poland,

Bibliografia

• [1] D. Banaszewski, On some subclasses of DB1 functions, Problemy Mat. 13 (1993), 33-41.
• [2] A. M. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. no. 659, Springer Verlag, Berlin-Heidelberg-New York (1978).
• [3] Z. Grande, T. Natkaniec, Lattices generated by F-quasi-continuous functions, Polish Acad. Sci. Math. 34 (1986), 525-530.
• [4] Z. Grande, L. Sołtysik, Some remarks on quasi-continuous real functions, Problemy Mat. 10 (1990), 79-86.
• [5] J. M. Jastrzębski, J. M. Jędrzejewski, T. Natkaniec, On some subclasses of Darboux functions, Fund. Math. 138 (1991), no. 3, 165-173.
• [6] R. Menkyna, The maximal additive and multiplicative families for functions with closed graph, Act. Math. Univ. Com. 52/53 (1987), 149-152.
• [7] T. Natkaniec, On quasi-continuous functions having Darboux property, Math. Pannon. 3 (1992), 81-96.
• [8] T. Radakovič, Uber Darbouxsche und stetige Funktionen, Monatsh. Math. Phys. 38 (1931), 117-122.
• [9] P. Szczuka, Maximal classes for the family of strong Świątkowski functions, Real Anal. Exchange 28 (2) (2003), 429-438.