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: 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