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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2008; 45(1): 221-228

Printed January 1, 2008

Copyright © The Korean Mathematical Society.

Topological complexity of semigroup actions

Xinhua Yan and Lianfa He

Hebei Normal University, Hebei Normal University

Abstract

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In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.

Keywords: topological complexity function, scattering, weak mixing

MSC numbers: 37B05,54H20

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