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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Compact group topologies for $ R$


Author: Douglas Hawley
Journal: Proc. Amer. Math. Soc. 30 (1971), 566-572
MSC: Primary 22.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0281834-5
MathSciNet review: 0281834
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Abstract: There is a compact solenoidal group S that is group isomorphic to the additive real numbers R. The existence of S leads to a study of compact real groups; that is, compact groups which are group isomorphic to R. The compact real groups are characterized as products of S. Various conditions on a topological group G are given which are equivalent to G being compact real. It is shown that any compact real group is solenoidal, connected and separable. Many sets and functions on R which are measurable with respect to the usual topology are shown to be nonmeasurable with respect to any compact group topology.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0281834-5
Article copyright: © Copyright 1971 American Mathematical Society