Real Analysis Exchange

Continuity Points of Typical Bounded Functions

Shingo Saito

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Kostyrko and Šalát showed that if a linear space of bounded functions has an element that is discontinuous almost everywhere, then a typical element in the space is discontinuous almost everywhere. We give a topological analogue of this theorem and provide some examples.

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Real Anal. Exchange, Volume 34, Number 1 (2008), 249-254.

First available in Project Euclid: 19 May 2009

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Mathematical Reviews number (MathSciNet)

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}
Secondary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

continuity points typical functions


Saito, Shingo. Continuity Points of Typical Bounded Functions. Real Anal. Exchange 34 (2008), no. 1, 249--254.

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