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http://dx.doi.org/10.4134/CKMS.c180365

A NOTE ON EXPANSIVE ℤk-ACTION AND GENERATORS  

Shah, Ekta (Department of Mathematics Faculty of Science The Maharaja Sayajirao University of Baroda)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.4, 2019 , pp. 1329-1334 More about this Journal
Abstract
We define the concept of a generator for a ${\mathbb{Z}}^k$-action T and show that T is expansive if and only it has a generator. Further, we prove several properties of a ${\mathbb{Z}}^k$-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;
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