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Compact groups and products of the unit interval

Published online by Cambridge University Press:  24 October 2008

Joan Cleary  and
Sidney A. Morris
Joan Cleary
Affiliation:
The University of Wollongong, Wollongong, N.S.W. 2500, Australia
Sidney A. Morris
Affiliation:
The University of New England, Armidale, N.S.W. 2351, Australia
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Extract

It is proved that if G is a compact connected Hausdorff group of uncountable weight, w(G), then G contains a homeomorphic copy of [0, 1]w(G). From this it is deduced that such a group, G, contains a homeomorphic copy of every compact Hausdorff group with weight w(G) or less. It is also deduced that every infinite compact Hausdorff group G contains a Cantor cube of weight w(G), and hence has [0, 1]w(G) as a quotient space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 293 - 297
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Chandler, R. E.. Hausdorff Compactifications (Marcel Dekker, 1976).Google Scholar
[2]Joan, Cleary and Morris, Sidney A.. Trinity – a tale of three cardinals. Proc. Centre Math. Anal. Austral. Nat. Univ. 14 (1986), 117–127.Google Scholar
[3]Ryszard, Engelking. General Topology (Polish Scientific Publishers, 1977).Google Scholar
[4]László, Fuchs. Infinite Abelian Groups (Academic Press, 1970).Google Scholar
[5]Edwin, Hewitt and Ross, Kenneth A.. Abstract Harmonic Analysis I (Springer-Verlag, 1963).Google Scholar
[6]Edwin, Hewitt and Ross, Kenneth A.. Abstract Harmonic Analysis II (Springer-Verlag, 1970).Google Scholar
[7]Jameson, G.. Topology and Normed Spaces (Chapman and Hall, 1974).Google Scholar
[8]Juhász, I.. Cardinal Functions in Topology – Ten Years Later (Mathematisch Centrum, Amsterdam, 1983).Google Scholar
[9]Kunen, K. and Vaughan, J. E. (eds). Handbook of Set-theoretical Topology (North-Holland, 1984).Google Scholar
[10]Montgomery, D. and Zippin, L.. Topological Transformation Groups (Interscience, 1965).Google Scholar
[11]Morris, Sidney A.. Pontryagin Duality and the Structure of Locally Compact Abelian Groups (Cambridge University Press, 1977).CrossRefGoogle Scholar
[12]Mostert, Paul. S.. Sections in principal fibre spaces. Duke Math. J. 23 (1956), 57–71.CrossRefGoogle Scholar
[13]Price, John F.. Lie Groups and Compact Groups (Cambridge University Press, 1977).CrossRefGoogle Scholar
[14]Walker, Russell C.. The Stone-Čech Compactification (Springer-Verlag, 1974).CrossRefGoogle Scholar