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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the representation of nonseparable analytic sets


Author: R. W. Hansell
Journal: Proc. Amer. Math. Soc. 39 (1973), 402-408
MSC: Primary 54H05
DOI: https://doi.org/10.1090/S0002-9939-1973-0380752-3
MathSciNet review: 0380752
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Abstract: Recently, the author considered extending the concepts of a Borel and analytic set for nonseparable metric spaces by allowing $ \sigma $-discrete families to replace countable families in the classical definitions. The resulting class of ``extended Borel sets'' was shown to lead to a new class of sets, intermediate to the Borel and analytic sets. In the present paper we show that the corresponding class of ``extended analytic sets'' does not lead to a new class of sets but actually coincides with the standard class of analytic sets. Thus their importance lies in the fact that they provide a useful ``representation'' for the analytic sets in arbitrary spaces. Several such representations are shown to lead to the same class of analytic sets.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0380752-3
Keywords: Analytic set, Borel set, $ k$-Souslin representations
Article copyright: © Copyright 1973 American Mathematical Society