International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 207016, 18 pages
Research Article

The Characterizations of Extreme Amenability of Locally Compact Semigroups

Hashem Masiha

Department of Mathematics, Faculty of Science, K. N. Toosi University of Technology, P.O. Box 16315 - 1618, Tehran 19697, Iran

Received 15 May 2008; Revised 22 August 2008; Accepted 10 November 2008

Academic Editor: Michael Tom

Copyright © 2008 Hashem Masiha. 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.


We demonstrate that the characterizations of topological extreme amenability. In particular, we prove that for every locally compact semigroup S with a right identity, the condition μ(F×G)=(μF)×(μG), for F, G in M(S), and 0<μM(S), implies that μ=εa, for some aS (εa is a Dirac measure). We also obtain the conditions for which M(S) is topologically extremely left amenable.