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Cardinalities of locally compact groups and their Stone-Čech compactifications

Published online by Cambridge University Press:  17 April 2009

Gerald L. Itzkowitz ,
Sidney A. Morris  and
Vladimir V. Tkachuk
Gerald L. Itzkowitz
Affiliation:
Department of Mathematics, Queens College, The City University of New York, Flushing, N.Y., 11367, United States of America e-mail: zev@forbin.qc.edu
Sidney A. Morris
Affiliation:
School of Information Technology and Mathematical Sciences, University of Ballarat, P.O. Box 663, Ballarat, Vic. 3353, Australias.morris@ballarat.edu.au
Vladimir V. Tkachuk
Affiliation:
Departmento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. VicentinaIztapalapa, C.P. 09340México D.F., e-mail: vova@xanum.uam.mx
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Abstract

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Dedicated to Edwin Hewitt

If G is any Hausdorff topological group and βG is the Stone-Čech compactification then where |G| denotes the cardinalty of G It is known that if G is a discrete group then and if G is the additive group of real numbers with the Euclidean topology, then |βG| = 2|G|. In this paper the cardinality and weight of βG, for a locally compact group G, is calculated in terms of the character and Lindelöf degree of G The results make it possible to give a reasonably complete description of locally compact groups G for which |βG| = 2|G| or even |βG| = |G|.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 353 - 364
Copyright
Copyright © Australian Mathematical Society 2003

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