Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systems
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systemsDate
2008Publisher
Springer VerlagISSN
09335846Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/acceptedVersionSubject
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 ... [+]
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 spaces [-]
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