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:
INVESTIGACIONMetadatos
Título
Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systemsFecha de publicación
2008Editor
Springer VerlagISSN
09335846Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/acceptedVersionPalabras clave / Materias
Resumen
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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