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On Abelian continuous groups

Published online by Cambridge University Press:  24 October 2008

M. H. A. Newman
Affiliation:
St John's College

Extract

An abstract continuous group, G, is an abstract space whose points have a continuous associative multiplication law, with division. The object of this note is to sketch a proof, which will appear in full elsewhere, that if the space G is locally Cartesian and compact, and the group G is Abelian (commutative), then G is the ordinary closed translation group in n dimensions: i.e. the space is that obtained from the “cube”

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1931

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References

* Newman, , Quarterly Journal of Math. 2 (1931), 18.CrossRefGoogle Scholar

* Abh. Hamburg Seminar, 4 (1925), 37.Google Scholar