On sets determined by sequences of quasi-continuous functions

• Autorzy: Wesołowska J.
• Języki publikacji: EN

Abstrakty

EN

The aim of the paper is to characterize those sets of points at which sequence of real functions from a given class F converges as well as sets of points of convergence to infinity of such sequences. As F we consider quasi-continuous functions and some other subclasses of Baire measurable functions.

Słowa kluczowe

EN

sequence of functions; sets of convergence points; quasi-continuity; cliquishness; simple continuity

PL

ciąg funkcji; zbiory punktów zbieżności; quasi-ciągłość; prosta ciągłość

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 2
• Strony: 271--283
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Wesołowska J.

• Institute of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland,

Bibliografia

• [1] Borsik, J., Limit of simply continuous functions, Real Anal. Exchange 18 (1992- 93), 270-275.
• [2] Kechris, A. S., Classical Descriptive Set Theory, Springer-Verlag, New York, 1995.
• [3] Kuratowski, K., Topologie, Vol 1, PWN, Warszawa, 1958.
• [4] Lipiński, J. S., Sets of points of convergence to infinity of a sequence of continuous functions (in Russian), Fund. Math. 51 (1962), 35-43.
• [5] Lunina, M. A., Sets of convergence and divergence of a sequences of real-valued continuous functions on a metric space (in Russian), Mat. Zametki 17 (1975), 205-217.
• [6] Natkaniec, T., On the maximum and the minimum of quasi-continuous functions, Math. Slovaca 42 (1992), 103-110.
• [7] Neubrunnová, A., On certain generalizations of the notion of continuity, Mat. Časopis. 23 (1973), 374-380.
• [8] Oxtoby, J., Measure and Category, Springer-Verlag, New York, 1971.
• [9] Sierpiński, W., Sur Tensemble des points de convergence d’une suite de fonctions continues, Fund. Math. 2 (1921), 41-49.
• [10] Wesołowska, J., On sets of convergence points of sequences of some real functions, Real Anal. Exchange 25(2) (1999-2000), 937-942.