On the Relation Between Left Thickness and Topological Left Thickness in Semigroups

James C. S. Wong
1982 Proceedings of the American Mathematical Society  
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 5 iff a certain subset Mt associated with T is left thick in a semigroup Si containing S, or equivalent, iff My contains a left ideal of Si. Our results contain a topological analogue of a result of H. Junghenn in [Amenability of function spaces on thick subsemigroups, Proc. Amer.
more » ... ups, 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 Mt is left thick iff it contains a left ideal in Si is quite surprising, since in general, a left thick subset need not contain a left ideal although the converse is always true.
doi:10.2307/2044451 fatcat:45ulburvuves7nlw5ty73yx2te