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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the relation between left thickness and topological left thickness in semigroups
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by James C. S. Wong PDF
Proc. Amer. Math. Soc. 86 (1982), 471-476 Request permission

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.
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Additional 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