Regulated Functions on Topological Spaces

Abstract

A regulated function on the real line is a real valued function whose left-hand and right-hand limits exist at all points. In this paper we examine a generalization of regulated functions to functions defined on Davison Spaces, which are topological spaces with a little extra structure. Properties of such functions are discussed. Our main result concerns the set of discontinuities of these functions. We also prove that regulated functions defined on the natural numbers, with the cofinite topology, coincide with convergent sequences.