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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.

References [Enhancements On Off] (What's this?)

  • [BFT] J. Bourgain, D. H. Fremlin, and M. Talagrand, Pointwise compact sets of Baire measurable functions, Amer. J. Math. 100 (1978), 845-885. MR 509077 (80b:54017)
  • [K] K. Kuratowski, Topology, Academic Press, New York, 1966. MR 0217751 (36:840)
  • [Ma] W. Marciszewski, On the classification of pointwise compact sets of the first Baire class functions, Fund. Math. 133 (1989), 165-209. MR 1065902 (91k:54026)
  • [Mi] A. W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114. MR 613787 (84e:03058a)
  • [Mo] Y. N. Moschovakis, Descriptive set theory, North-Holland, Amsterdam, 1979. MR 561709 (82e:03002)
  • [P1] R. Pol, Note on pointwise convergence of sequences of analytic sets, Matematika 36 (1989), 290-300 MR 1045789 (91j:54070)
  • [P2] -On pointwise and weak topology in function spaces, preprint.
  • [R] H. P.Rosenthal, A characterization of Banach spaces containing $ {l_1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411-2413. MR 0358307 (50:10773)

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