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 A note on expansive $\mathbb{Z}^k$-action and generators Commun. Korean Math. Soc. 2019 Vol. 34, No. 4, 1329-1334 https://doi.org/10.4134/CKMS.c180365Published online October 31, 2019 Ekta Shah The Maharaja Sayajirao University of Baroda 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 MSC numbers : Primary 37B99; Secondary 54H20 Downloads: Full-text PDF   Full-text HTML