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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
DOI: https://doi.org/10.1090/S0002-9939-1982-0660616-3
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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Keywords: Baire measurable selections, compact groups, Bockstein separation property
Article copyright: © Copyright 1982 American Mathematical Society