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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Baire sections for group homomorphisms


Authors: S. Graf and G. Mägerl
Journal: Proc. Amer. Math. Soc. 85 (1982), 615-618
MSC: Primary 54C65; Secondary 22C05, 28B20, 54C50
MathSciNet review: 660616
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Abstract: The following result is proved: Let $ X$ and $ Y$ be compact topological groups and $ p$ be a continuous group homomorphism from $ Y$ onto $ X$. Then there exists a map $ q$ from $ X$ to $ Y$ such that $ p \circ q = {\text{i}}{{\text{d}}_X}$ and $ {q^{ - 1}}(B)$ is a Baire set in $ Y$ for every Baire subset $ B$ of $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660616-3
PII: S 0002-9939(1982)0660616-3
Keywords: Baire measurable selections, compact groups, Bockstein separation property
Article copyright: © Copyright 1982 American Mathematical Society