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oaioai:repositori.uji.es:10234/14153

Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systems

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Publication date
1 January 2008
Publisher
Springer Verlag
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    Abstract

    It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known. In this note we construct, in ZFC, 2c non-metrizable infinite pairwise nonhomeomorphic minimal sets on compact connected linearly ordered space

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    Repositori Institucional de la Universitat Jaume I

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    Last time updated on 17/11/2016

    This paper was published in Repositori Institucional de la Universitat Jaume I.

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