Thickly syndetic sensitivity of semigroup actions
Bull. Korean Math. Soc. 2018 Vol. 55, No. 4, 1125-1135
Published online March 8, 2018
Printed July 31, 2018
Huoyun Wang
Guangzhou University
Abstract : 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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