Topology Proceedings
Document # baao-35
Topology Proceedings 33 (2009), pp. 55-79 |
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Sets central with respect to certain subsemigroups of bSd
Dibyendu De, Neil Hindman and Dona Strauss
Central sets in a semigroup S are most simply
characterized as members of minimal idempotents in the Stone-Cech
compactification bSd of S with the discrete topology. They are
known to have remarkably strong combinatorial properties. In this paper
we concentrate on members of idempotents in compact subsemigroups T of
bSd. We show that under reasonable hypotheses any member of a
minimal idempotent in T is in fact a member of many distinct minimal
idempotents in T. And we show that under certain assumptions which occur
quite widely, the subsets of S whose closures contain T must contain
images of all first entries matrices. For example, all of our results
apply to the case in which (S, +) is a commutative cancellative
topological semigroup with an identity and T is the set of ultrafilters
on S which converge to the identity.
Keywords: central sets, compact subsemigroups, image partition regular matrices
Mathematics Subject Classification: 54D35 (22A15 05D10 54D80)
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Topology Proceedings,
Volume 33 (2009)
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