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1997/1998 On a Conjecture of Agronsky and Ceder Concerning Orbit-Enclosing \(\omega\)-Limit Sets
Marta Babilonová
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Real Anal. Exchange 23(2): 773-778 (1997/1998).


In 1991, Agronsky and Cedar made the following conjecture: A continuum \(K \subset E^{k}\) is an orbit-enclosing \(\omega\)-limit set if and only if it is arcwise connected. The main aim of this paper is to disprove this conjecture by giving an example of an orbit-enclosing \(\omega\)-limit set \(S\) in \(E^{2}\) (cf. Theorem 3 below) which is not arcwise connected. Moreover, we show that \(S\) can be chosen with non-empty interior, and the mapping \(F\), with respect to which \(S\) is an orbit-enclosing \(\omega\)-limit set can be chosen as a triangular map.


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Marta Babilonová. "On a Conjecture of Agronsky and Ceder Concerning Orbit-Enclosing \(\omega\)-Limit Sets." Real Anal. Exchange 23 (2) 773 - 778, 1997/1998.


Published: 1997/1998
First available in Project Euclid: 14 May 2012

zbMATH: 0939.37013
MathSciNet: MR1639969

Primary: 26A18 , 58F12
Secondary: 58F08

Keywords: {arcwise connected continuum} , {omega-limit set} , {orbit-enclosing omega-limit set} , {topological transitivity} , {triangular map}

Rights: Copyright © 1999 Michigan State University Press

Vol.23 • No. 2 • 1997/1998
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