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$ F\sb \sigma$-set covers of analytic spaces and first class selectors


Author: R. W. Hansell
Journal: Proc. Amer. Math. Soc. 96 (1986), 365-371
MSC: Primary 54H05; Secondary 28A05, 54C65
DOI: https://doi.org/10.1090/S0002-9939-1986-0818473-1
MathSciNet review: 818473
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Abstract: Let $ X$ be an analytic space (e.g., a complete metric space). We prove that any point-countable $ {F_\sigma }$-set cover of $ X$ either has $ \sigma $-discrete refinement, or else there is a compact subset of $ X$ not covered by any countable subfamily of the cover. It follows that any point-countable $ {F_\sigma }$-additive family in $ X$ has a $ \sigma $-discrete refinement. This is used to show that any weakly $ {F_\sigma }$-measurable multimap, defined on $ X$ and taking nonempty, closed and separable values in a complete metric space, has a selector of the first Baire class.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0818473-1
Keywords: Analytic space, $ \sigma $-discrete refinement, first class selectors, $ {F_\sigma }$-additive family
Article copyright: © Copyright 1986 American Mathematical Society

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