Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systems
نویسندگان
چکیده
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 Z FC , 2c non-metrizable infinite pairwise nonhomeomorphic minimal sets on compact connected linearly ordered spaces.
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ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 47 شماره
صفحات -
تاریخ انتشار 2008