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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

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