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1996/1997 A symmetrically continuous function which is not countably continuous
Krzysztof Ciesielski, Marcin Szyszkowski
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Real Anal. Exchange 22(1): 428-432 (1996/1997).


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.


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Krzysztof Ciesielski. Marcin Szyszkowski. "A symmetrically continuous function which is not countably continuous." Real Anal. Exchange 22 (1) 428 - 432, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 1 June 2012

zbMATH: 0879.26010
MathSciNet: MR1433629

Primary: 26A15
Secondary: 26A03

Keywords: countable continuity , Sierpiński-Zygmund functions , symmetric continuity

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
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