On the Rosenthal compacta and analytic sets
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- by Adam Krawczyk
- Proc. Amer. Math. Soc. 115 (1992), 1095-1100
- DOI: https://doi.org/10.1090/S0002-9939-1992-1086583-5
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Abstract:
We consider pointwise convergence in a separable Rosenthal compactum. The main result is that if $X \subset {{\mathbf {R}}^{{\omega ^\omega }}}$ is a Rosenthal compactum, $Y \subset X$ is countable dense and $x \in X$, then the following are equivalent: (i) $Y$ has a countable base at $x$. (ii) $\{ ({Y_i}) \in {Y^\omega }:{\lim _{i \to \infty }}{y_i} = x\}$ is analytic, when $Y$ has the discrete topology.References
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Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 1095-1100
- MSC: Primary 54H05
- DOI: https://doi.org/10.1090/S0002-9939-1992-1086583-5
- MathSciNet review: 1086583