A theorem on function spaces
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- by Jan Baars, Joost de Groot and Jan van Mill PDF
- Proc. Amer. Math. Soc. 105 (1989), 1020-1024 Request permission
Abstract:
Let $X$ and $Y$ be normal and first countable spaces, such that ${C_p}(X)$ and ${C_p}(Y)$ are linearly homeomorphic. Suppose ${X^{(\alpha )}}$ is countably compact for some $\alpha < {\omega _1}$. We prove that if $\alpha = 1$ then ${Y^{(\alpha )}}$ is also countably compact. The first countability condition in this result is essential. We also present examples that if $\alpha$ is not a prime component, then ${Y^{(\alpha )}}$ need not to be countably compact.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 1020-1024
- MSC: Primary 54C35; Secondary 54A25
- DOI: https://doi.org/10.1090/S0002-9939-1989-0943792-0
- MathSciNet review: 943792