ON THE CONVERGENCE OF SEQUENCES OF FUNCTIONS WHICH ARE DISCONTINUOUS ON COUNTABLE SETS

Let (X, T-X) be a topological space and let (Y, d(Y)) 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}, H-1(X, Y) = {f : X -> Y; there exists(h subset of C(X,Y)) {x; f(x) not equal h(x)} is countable}, and H-2(X, Y) = H(X,Y)boolean AND H-1(X, Y). In this article we investigate some convergences (pointwise, uniform, quasiuniform, discrete and trans fi nite) of sequences of functions from H(X, Y), H-1(X, Y) and H-2(X, Y).