Function spaces of low Borel complexity
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- by J. Dijkstra, T. Grilliot, D. Lutzer and J. van Mill PDF
- Proc. Amer. Math. Soc. 94 (1985), 703-710 Request permission
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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 703-710
- MSC: Primary 54C35; Secondary 54C50, 54H05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0792287-2
- MathSciNet review: 792287