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On a question of Archangelskij concerning Lindelöf spaces with countable pseudocharacter


Author: K. Alster
Journal: Proc. Amer. Math. Soc. 95 (1985), 320-322
MSC: Primary 54D20; Secondary 54A25
DOI: https://doi.org/10.1090/S0002-9939-1985-0801347-9
MathSciNet review: 801347
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Abstract: We give a negative solution to Archangelskij's problem by showing that there exists a Lindelöf space with countable pseudocharacter which does not admit a continuous one-to-one mapping onto a first countable Hausdorff space.


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

  • [A1] K. Alster, Some remarks on another Michael's problem concerning the Lindelöf property in the Cartesian products (in preparation).
  • [Ar] A. V. Archangelskij, On cardinal invariants, General Topology and its Relations to Modern Analysis and Algebra. III (Proc. Third Prague Topological Sympos. 1971), Academia, Prague, 1972, pp. 37-45. MR 0410629 (53:14377)
  • [C] H. H. Corson, The weak topology of Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15. MR 0132375 (24:A2220)
  • [HJ] A. Hajnal and I. Juhász, Lindelöf spaces a la Shelah, Colloq. Math. Soc. János Bolyai 23 (1978), 555-567. MR 588804 (82h:03053)
  • [J] T. J. Jech, Lectures in set theory with particular emphasis on the method of forcing, Lecture Notes in Math., vol. 217, Springer-Verlag, 1971. MR 0321738 (48:105)
  • [S] S. Shelah, Handwritten notes, 1978.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0801347-9
Article copyright: © Copyright 1985 American Mathematical Society

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