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(1991)
Some limitations toward extending ˘ Sarkovski˘ ı's theorem to connected linearly ordered spaces
D. Chillingworth (1995)
THE GENERAL TOPOLOGY OF DYNAMICAL SYSTEMSBulletin of The London Mathematical Society, 27
D. Alcaraz, M. Sanchis (2003)
A Note on Sarkovskii's Theorem in Connected Linearly Ordered SpacesInt. J. Bifurc. Chaos, 13
M. Pollicott, M. Yuri (1998)
Dynamical Systems and Ergodic Theory
Louis Block, W. Coppel (1992)
Dynamics in One Dimension
(1985)
A topologist's view of ˘ Sarkovski˘ ı's theorem
R. Engelking (1977)
General topology
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, $${2^{\mathfrak{c}}}$$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces.
Archive for Mathematical Logic – Springer Journals
Published: Jun 17, 2008
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