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1995/1996 Scattered sets, chains and the Baire Category Theorem
C. Freiling, B. S. Thomson
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Real Anal. Exchange 21(2): 440-458 (1995/1996).


A scattered set of real numbers can be exhibited in terms of endpoints of the components of some nondecreasing sequence of open sets (chain). We study this connection between scattered sets and chains providing characterizations of scattered sets, semiscattered sets, certain splattered sets and sets with countable closure. It is shown that any application of the Baire Category Theorem on the real line leads naturally to a chain of open sets and hence to an exceptional scattered set. Some applications of this fact are given.


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C. Freiling. B. S. Thomson. "Scattered sets, chains and the Baire Category Theorem." Real Anal. Exchange 21 (2) 440 - 458, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 14 June 2012

zbMATH: 0879.54043
MathSciNet: MR1407261

Primary: 26A21
Secondary: 54E52

Keywords: Baire category theorem , scattered set

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 2 • 1995/1996
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