Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	M. Hrušák M. Sanchis Á. Tamariz-Mascarúa

Affiliation:	(1) Instituto de Matemáticas, Universidad Nacional Autónoma de México, Xangari, 58089 Morelia Michoacan, Mexico;(2) Departament de Matemàtiques, Universitat Jaume I, Campus de Riu Sec s/n, 8029, AP, Castelló, Spain;(3) Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 México, Mexico

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, ${2^{mathfrak{c}}}$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces.

Keywords:	Dynamical system Minimal set Cantor set Linearly ordered topological space
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