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Proceedings of the American Mathematical Society

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

 

 

The topological spaces that support Haar systems


Authors: Scott McCullough and Daniel Wulbert
Journal: Proc. Amer. Math. Soc. 94 (1985), 687-692
MSC: Primary 41A52; Secondary 41A45, 41A65
DOI: https://doi.org/10.1090/S0002-9939-1985-0792284-7
MathSciNet review: 792284
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Abstract: A topological space $ X$ supports a nontrivial Haar system if and only if there is a continuous one-to-one map of $ X$ into the unit circle. This gives an elementary proof of Mairhuber's classical theorem for compact $ X$. It answers a 1960 question asked by R. R. Phelps when $ X$ is locally compact.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0792284-7
Keywords: Mairhuber's Theorem
Article copyright: © Copyright 1985 American Mathematical Society