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International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 733-740
http://dx.doi.org/10.1155/S0161171292000954

Recurrent points and discrete points for elementary amenable groups

Jodrey School of Computer Science, Acadia University, Nova Scotia, Wolfville B0P 1X0, Canada

Received 18 January 1989; Revised 31 March 1992

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let βG be the Stone-Cech compactification of a group G, AG the set of all almost periodic points in βG, KG=c[{suppμφ:φLIM(G)}] and RG the set of all recurrent points in βG. In this paper we will study the relationships between KG and RG, and between AG and RG. We will show that for any infinite elementary amenable group G, AGRG and RGKGϕ.