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- W4297799427 abstract "When a topological group $G$ acts on a compact space $X$, its enveloping semigroup $E(X)$ is the closure of the set of $g$-translations, $gin G$, in the compact space $X^X$. Assume that $X$ is metrizable. It has recently been shown by the first two authors that the following conditions are equivalent: (1) $X$ is hereditarily almost equicontinuous; (2) $X$ is hereditarily non-sensitive; (3) for any compatible metric $d$ on $X$ the metric $d_G(x,y):=sup{d(gx,gy): gin G}$ defines a separable topology on $X$; (4) the dynamical system $(G,X)$ admits a proper representation on an Asplund Banach space. We prove that these conditions are also equivalent to the following: the enveloping semigroup $E(X)$ is metrizable." @default.
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- W4297799427 date "2006-06-15" @default.
- W4297799427 modified "2023-09-26" @default.
- W4297799427 title "On metrizable enveloping semigroups" @default.
- W4297799427 doi "https://doi.org/10.48550/arxiv.math/0606373" @default.
- W4297799427 hasPublicationYear "2006" @default.
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