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
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