A note on Expansive $\mathbb{Z}^k$-$action and generators
Commun. Korean Math. Soc.
Published online April 12, 2019
Ekta Shah
The Maharaja Sayajirao University of Baroda
Abstract : We define the concept of a generator for $\mathbb{Z}^k-$action $T$ and show that $T$ is expansive if and only it has a generator. Further, we prove several properties of $\mathbb{Z}^k-$action including that the least upper bound of the set of expansive constants is not an expansive constant.
Keywords : Expansive homeomorphisms, generators, $\mathbb{Z}^k-$actions
MSC numbers : Primary 37B99, Secondary 54H20
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd