Remarks on Generalized Metric Discrete Convergence Spaces

Abstract

Ez, ... be arbitrary non-empty sets and t be a mapping of E into P( U n En), " € 8 2 ?aF"where P(U) denotes the power set of U. Suppose that (~~)~~~, c t ( s ) ( w i t h k c %and with x , € E , for every n c N ' ) and N+%N' imply ( X , ) , €~+ E T ( . ) . Then X = = ( ( E , El, Ez, ...), t ) is called a discrete convergence space and t its discrete convergence. Frequently instead of ( x , , ) , ,~~, c t(.) we write ( x~)~~~ 7 x and say that ( z , )~~ N, converges discretely (to x).