Enveloping semigroups and mappings onto the two-shift

Berg, Kenneth; Gove, David; Haddad, Kamel

doi:10.1090/S0002-9939-98-04185-9

Enveloping semigroups and mappings onto the two-shift
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by Kenneth Berg, David Gove and Kamel Haddad PDF

Proc. Amer. Math. Soc. 126 (1998), 899-905 Request permission

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-Čech 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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