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2007/2008 Regulated Functions on Topological Spaces
Julie O’Donovan
Real Anal. Exchange 33(2): 405-416 (2007/2008).


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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Julie O’Donovan. "Regulated Functions on Topological Spaces." Real Anal. Exchange 33 (2) 405 - 416, 2007/2008.


Published: 2007/2008
First available in Project Euclid: 18 December 2008

zbMATH: 1158.26002
MathSciNet: MR2458257

Primary: 26A15 , 54C35‎

Keywords: discontinuous functions , regulated functions

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 2 • 2007/2008
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