Real Analysis Exchange

A symmetrically continuous function which is not countably continuous

Krzysztof Ciesielski and Marcin Szyszkowski

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Abstract

We construct a symmetrically continuous function \(f\colon\mathbb{R}\to\mathbb{R}\) such that for some \(X\subset\mathbb{R}\) of cardinality continuum \(f|X\) is of Sierpiński-Zygmund type. In particular such an \(f\) is not countably continuous. This gives an answer to a question of Lee Larson.

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 428-432.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515236

Mathematical Reviews number (MathSciNet)
MR1433629

Zentralblatt MATH identifier
0879.26010

Subjects
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: 26A03: Foundations: limits and generalizations, elementary topology of the line

Keywords
symmetric continuity countable continuity Sierpiński-Zygmund functions

Citation

Ciesielski, Krzysztof; Szyszkowski, Marcin. A symmetrically continuous function which is not countably continuous. Real Anal. Exchange 22 (1996), no. 1, 428--432. https://projecteuclid.org/euclid.rae/1338515236


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