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On the Rosenthal compacta and analytic sets


Author: Adam Krawczyk
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
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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 [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1992-1086583-5
Article copyright: © Copyright 1992 American Mathematical Society

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