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Proceedings of the American Mathematical Society

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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$.

References [Enhancements On Off] (What's this?)

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Keywords: Baire measurable selections, compact groups, Bockstein separation property
Article copyright: © Copyright 1982 American Mathematical Society

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