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A theorem on the Bohr compactification of a locally compact Abelian group

Published online by Cambridge University Press:  24 October 2008

N. Th. Varopoulos
Affiliation:
Trinity College, Cambridge

Extract

Notations. If G denotes an Abelian group and L a locally compact group topology on G, G(L) will denote the resulting topological group, and will denote the character group with the usual Pontrjagin topology (which is locally compact). Rn will denote the real n-dimensional vector group. Finally, for any set X, |X| will denote its cardinal number.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Bourbaki, N.Topologie générate (Hermann; Paris, 1961).Google Scholar
(2)Bourbaki, N.Intégration (Hermann; Paris, 1953).Google Scholar
(3)Glicksberg, I.Canad. J. Math. 14 (1962), 269276.CrossRefGoogle Scholar
(4)Hewitt, E.Fund. Math. 53 (1963), 5564.CrossRefGoogle Scholar
(5)Montgomery, D and Zippin, L.Topological transformation groups (Interscience; New York, 1955).Google Scholar
(6)Naimark, M. A.Normed rings (Noordhoff; Groningen, 1959).Google Scholar
(7)Northcott, D. G.An introduction to homological algebra (Cambridge, 1960).CrossRefGoogle Scholar
(8)Ross, K.Closed subgroups of locally compact Abelian groups. Fund. Math., (to appear).Google Scholar
(9)Rudin, W.Fourier analysis on groups. (Interscience; New York, 1962).Google Scholar
(10)Varopoulos, N. Th.Studies in harmonic analysis. Proc. Cambridge Philos. Soc. 60 (1964), 465516.CrossRefGoogle Scholar
(11)Well, A.L'intégration dans les groupes topologiques et ses applications (Hermann; Paris, 1940).Google Scholar