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On sequences of upper and lower semi-quasicontinuous functions

100%

Grande Z.

tom Vol. 7, nr 2

235-242

In this article we investigate the pointwise, discrete and transfinite convergences in the classes of real functions defined on topological spaces which are upper and lower quasicontinuous at each point.

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

63%

Grande Z. , Strońska E.

tom Vol. 11, nr 2

247-259

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).