On the relation between left thickness and topological left thickness in semigroups

Author:

Wong James C. S.

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 T of a locally compact semigroup S S is topological left thick in S S iff a certain subset M T {M_T} associated with T T is left thick in a semigroup S 1 {S_1} containing S S , or equivalent, iff M T {M_T} contains a left ideal of S 1 {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 {M_T} is left thick iff it contains a left ideal in S 1 {S_1} is quite surprising, since in general, a left thick subset need not contain a left ideal although the converse is always true.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

1. Lumpy subsets in left-amenable locally compact semigroups;Day, Mahlon M.;Pacific J. Math.,1976

2. \bysame, Left thick to left lumpy—a guided tour (to appear).

3. On lattices and algebras of real valued functions;Douglas, R. G.;Amer. Math. Monthly,1965

4. Amenability of function spaces on thick subsemigroups;Junghenn, H. D.;Proc. Amer. Math. Soc.,1979

5. Left thick subsets of a topological semigroup;Kharaghani, H.;Illinois J. Math.,1978

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Two open problems of Day and Wong on left thick subsets and left amenability;Journal of Mathematical Analysis and Applications;2017-08

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