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Proceedings of the American Mathematical Society

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

 

 

Function spaces of low Borel complexity


Authors: J. Dijkstra, T. Grilliot, D. Lutzer and J. van Mill
Journal: Proc. Amer. Math. Soc. 94 (1985), 703-710
MSC: Primary 54C35; Secondary 54C50, 54H05
MathSciNet review: 792287
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Abstract: In this paper we investigate situations in which the space $ {C_\pi }(X)$ of continuous, real-valued functions on $ X$ is a Borel subset of the product space $ {{\mathbf{R}}^X}$. We show that for completely regular, nondiscrete spaces, $ {C_\pi }(X)$ cannot be a $ {G_\delta }$, an $ {F_\sigma }$, or a $ {G_{\delta \sigma }}$ subset of $ {{\mathbf{R}}^X}$, but it can be an $ {F_{\sigma \delta }}$ or $ {G_{\delta \sigma \delta }}$ subset.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0792287-2
Article copyright: © Copyright 1985 American Mathematical Society