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Bull. Korean Math. Soc. 2018; 55(4): 1125-1135

Online first article March 8, 2018      Printed July 31, 2018

https://doi.org/10.4134/BKMS.b170622

Copyright © The Korean Mathematical Society.

Thickly syndetic sensitivity of semigroup actions

Huoyun Wang

Guangzhou University

Abstract

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We show that for an M-action on a compact Hausdorff uniform space, if it has at least two disjoint compact invariant subsets, then it is thickly syndetically sensitive. Additionally, we point out that for a P-M-action of a discrete abelian group on a compact Hausdorff uniform space, the multi-sensitivity is equivalent to both thick sensitivity and thickly syndetic sensitivity.

Keywords: semigroup action, thickly syndetic set, $M$-systems, sensitivity

MSC numbers: Primary 37B20, 37B05, 54H20

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