Compact groups and products of the unit interval
Published online by Cambridge University Press: 24 October 2008
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
References
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