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• W2050861566 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, g ∈ 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 nonsensitive; (3) for any compatible metric d on X the metric d G (x, y) ≔ sup{d(gx, gy): g ∈ 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.
• W2050861566 created "2016-06-24" @default.
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• W2050861566 date "2008-03-01" @default.
• W2050861566 modified "2023-09-26" @default.
• W2050861566 title "On metrizable enveloping semigroups" @default.
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• W2050861566 doi "https://doi.org/10.1007/s11856-008-0032-3" @default.
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