The topological spaces that support Haar systems

McCullough, Scott; Wulbert, Daniel

doi:10.1090/S0002-9939-1985-0792284-7

The topological spaces that support Haar systems
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by Scott McCullough and Daniel Wulbert

Proc. Amer. Math. Soc. 94 (1985), 687-692

DOI: https://doi.org/10.1090/S0002-9939-1985-0792284-7

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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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