On the relation between left thickness and topological left thickness in semigroups
Author:
James C. S. Wong
Journal:
Proc. Amer. Math. Soc. 86 (1982), 471-476
MSC:
Primary 43A07
DOI:
https://doi.org/10.1090/S0002-9939-1982-0671218-7
MathSciNet review:
671218
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we establish an interesting relation between left thickness and topological left thickness in semigroups by showing that a Borel subset of a locally compact semigroup
is topological left thick in
iff a certain subset
associated with
is left thick in a semigroup
containing
, or equivalent, iff
contains a left ideal of
. Our results contain a topological analogue of a result of H. Junghenn in [Amenability of function spaces on thick subsemigroups, Proc. Amer. Math. Soc. 75 (1979), 37-41]. However, even in the case of discrete semigroups, our results are more general and in a way more natural than those of Junghenn's. Furthermore, the fact that
is left thick iff it contains a left ideal in
is quite surprising, since in general, a left thick subset need not contain a left ideal although the converse is always true.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0671218-7
Keywords:
Locally compact semigroups,
convolution measure algebras,
topological left thickness and left thickness,
invariant means
Article copyright:
© Copyright 1982
American Mathematical Society