Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Enveloping semigroups and mappings onto the two-shift

Author(s): Kenneth Berg; David Gove; Kamel Haddad
Journal: Proc. Amer. Math. Soc. 126 (1998), 899-905.
MSC (1991): Primary 58F08, 58F03, 54H20
MathSciNet review: 1443145
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Abstract: Enveloping semigroups of topological actions of semigroups $G$ on compact spaces are studied. For zero dimensional spaces, and under modest conditions on $G$ , the enveloping semigroup is shown to be the Stone-\v{C}ech compactification if and only if some Cartesian product has the two-shift as a factor. Examples are discussed showing that, unlike in the measure theory case, positive entropy does not imply the existence of such a factor even if the Cartesian product has large entropy.

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