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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the Rosenthal compacta and analytic sets

Author: Adam Krawczyk
Journal: Proc. Amer. Math. Soc. 115 (1992), 1095-1100
MSC: Primary 54H05
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.

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PII: S 0002-9939(1992)1086583-5
Article copyright: © Copyright 1992 American Mathematical Society

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