A note on the quasicontinuity

• Autorzy: Grande Z.
• Języki publikacji: EN

Abstrakty

EN

Let (X,px) and (V, pv) be metric spaces. A function f: X - Y is said graph quasicontinuous if there is a quasicontinuous function g : X -> Y with the graph Gr(g) contained in the closure cl(Gr(f)) of Gr(f). If the space (V, pv) is compact and if there is a dense subset A C X such that the restricted function f/A is continuous then f is graph quasicontinuous. Moreover each locally bounded function f: R -> R is graph quasicontinuous.

Słowa kluczowe

EN

graphs; real functions; quasicontinuity; bounded functions

PL

grafy; funkcje rzeczywiste; funkcje ograniczone

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 3
• Strony: 515--518
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Grande Z.

• Institute of Mathematics Kazimierz Wielki University Pl. Weyssenhoffa 11 85-072 Bydgoszcz, Poland

Bibliografia

• [1] H. BlumbergH, New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), 113-128.
• [2] A. Mikucka, Graph quasi-continuity, Demonstratio Math., 36 (2003), 483-494.
• [3] A. Mikucka, Graph continuous functions and graph quasi-continuous functions (in Polish), Doctoral Thesis, Technical University Lodz 2004.
• [4] T. Neubrunn, Quasi-continuity, Real Anal. Exchange 14 No. 2 (1988-89), 259-306.