On the relation between left thickness and topological left thickness in semigroups
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- by James C. S. Wong
- Proc. Amer. Math. Soc. 86 (1982), 471-476
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671218-7
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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 $T$ of a locally compact semigroup $S$ is topological left thick in $S$ iff a certain subset ${M_T}$ associated with $T$ is left thick in a semigroup ${S_1}$ containing $S$, or equivalent, iff ${M_T}$ contains a left ideal of ${S_1}$. 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 ${M_T}$ is left thick iff it contains a left ideal in ${S_1}$ is quite surprising, since in general, a left thick subset need not contain a left ideal although the converse is always true.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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