Source: Real Anal. Exchange
Volume 33, Number 2
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.
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