On the convergence of sequences of functions which are discontinuous on countable sets

• Autorzy: Grande Z. , Strońska E.
• Języki publikacji: EN

Abstrakty

EN

Let (X, Tx) be a topological space and let (Y, dy) be a metric space. For a function f : X → y denote by C(f) the set of all continuity points of f and by D(f) = X\C(f) the set of all discontinuity points of f. Let C(X,Y) = {f : X → Y; f is continuous}, H(X, Y) = {f: X →Y; D{f) is countable}, H1(X, Y) = {f: X → Y; ∃h ∈c(x,Y) {x; f(x) ≠ h{x)} is countable}, and H2(X, Y) = H(X, Y) ∩ H1(X, Y). In this article we investigate some convergences (pointwise, uniform, quasiuniform, discrete and transfinite) of sequences of functions from H(X, Y), H1(X, Y) and H2(X, Y).

Słowa kluczowe

EN

Baire 1 class; density topology; quasiuniform convergence; discrete convergence; transfinite sequences

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2005
• Tom: Vol. 11, nr 2
• Strony: 247--259
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Grande Z.

• The University of Computer Science, TWP Olsztyn, Wyzwolenia 30, 10-106 Olsztyn, Poland

autor

Strońska E.

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

Bibliografia

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