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The ideal structure of the Stone-Čech compactification of a group

Published online by Cambridge University Press:  24 October 2008

J. W. Baker  and
P. Milnes
J. W. Baker
Affiliation:
University of Sheffield
P. Milnes
Affiliation:
University of Sheffield
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Extract

Let S be both a topological space and a semigroup. For s ∈ S, define the maps λs and ρs of S to S by

We shall say that S is a right-topological (resp. left-topological) semigroup if ρs (resp. λs) is continuous for each s in S. We denote by Λ(S) the set

this is a subsemigroup of S.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 3 , November 1977 , pp. 401 - 409
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Baker, J. W. and Butcher, R. J.The Stone-Čech compactification of a topological semi-group. Math. Proc. Cambridge Philos. Soc. 80 (1976), 103–107.CrossRefGoogle Scholar
(2)Berglund, J. F. and Hofmann, K. H. Compact semitopological semigroups and weakly almost periodic functions. Lecture Notes in Mathematics, no. 42 (Berlin: Springer-Verlag, 1967).Google Scholar
(3)Butcher, R. J. The Stone-Čech compactification of a topological semigroup, and its algebra of measures. Ph.D. thesis, University of Sheffield, 1975.Google Scholar
(4)Chou, C.Minimal sets and ergodic measures on βN\N. Illinois J. Math. 13 (1969), 777–788.CrossRefGoogle Scholar
(5)Chou, C.On the size of the set of left invariant means on a semigroup. Proc. Amer. Math. Soc. 23 (1969), 199–205.Google Scholar
(6)Chou, C.On a geometric property of the set of invariant means on a group. Proc. Amer. Math. Soc. 30 (1971), 296–302.CrossRefGoogle Scholar
(7)Chou, C.The exact cardinality of the set of invariant means on a group. Proc. Amer. Math. Soc. 55 (1976), 103–106.CrossRefGoogle Scholar
(8)Ellis, R.Lectures on topological dynamics, (New York, W. A. Benjamin, 1969).Google Scholar
(9)Hewitt, E. and Ross, K. A.Abstract Harmonic Analysis, vol. 1 (Berlin: Springer-Verlag, 1963).Google Scholar
(10)Macri, N.The continuity of the Arens product on the Stone-Čech compactification of semi-groups. Trans. Amer. Math. Soc. 191 (1974), 185–193.Google Scholar
(11)Milnes, P.Compactifications of semitopological semigroups. J. Australian Math. Soc. 15 (1973), 488–503.CrossRefGoogle Scholar
(12)Mitchell, T.Topological semigroups and fixed points. Illinois J. Math. 14 (1970), 630–641.CrossRefGoogle Scholar
(13)Rundin, W.Fourier analysis on groups (New York: John Wiley, 1962).Google Scholar
(14)Ruppert, W.Rechtstopologische Halbgruppen. J. Reine Angew. Math. 261 (1973), 123–133.Google Scholar
(15)Terras, R. Almost automorphic functions on topological groups. Ph.D. thesis, University of Illinois, 1970.Google Scholar