Real Analysis Exchange

Regulated Functions on Topological Spaces

Julie O’Donovan

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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.

Article information

Real Anal. Exchange Volume 33, Number 2 (2007), 405-416.

First available in Project Euclid: 18 December 2008

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Zentralblatt MATH identifier

Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 54C35: Function spaces [See also 46Exx, 58D15]

regulated functions discontinuous functions


O’Donovan, Julie. Regulated Functions on Topological Spaces. Real Anal. Exchange 33 (2007), no. 2, 405--416.

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