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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Enveloping semigroups and mappings
onto the two-shift


Authors: Kenneth Berg, David Gove and Kamel Haddad
Journal: Proc. Amer. Math. Soc. 126 (1998), 899-905
MSC (1991): Primary 58F08, 58F03, 54H20
DOI: https://doi.org/10.1090/S0002-9939-98-04185-9
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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Additional Information

Kenneth Berg
Affiliation: Department of Mathematics, University of Maryland at College Park, College Park, Maryland 20742
Email: krb@hroswitha.umd.edu

David Gove
Affiliation: Department of Mathematics, California State University at Bakersfield, Bakersfield, California 93311
Email: dgove@ultrix6.cs.csubak.edu

Kamel Haddad
Affiliation: Department of Mathematics, California State University at Bakersfield, Bakersfield, California 93311
Email: khaddad@ultrix6.cs.csubak.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04185-9
Keywords: Enveloping semigroup, subshift, topological action
Received by editor(s): August 29, 1996
Communicated by: Mary Rees
Article copyright: © Copyright 1998 American Mathematical Society