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On the product of relatively weakly almost Lindelöf subsets

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Abstract

The purpose of this note is to show that there exist two Tychonoff spaces X, Y, a subset A of X and a subset B of Y such that A is weakly almost Lindelöf in X and B is weakly almost Lindelöf in Y, but A × B is not weakly almost Lindelöf in X × Y.

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References

  1. A. V. Arhangel’skiĭ and M. M. Genedi Khamdi. The origin of the theory of relative topological properties, General Topology, Space and Mappings, 3–48, Moskov. Gos. Univ. (Moscow, 1989) (in Russian).

    Google Scholar 

  2. A. V. Arhangel’skiĭ, A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carolin., 36 (1995), 303–325.

    MathSciNet  Google Scholar 

  3. L. Block, On the product of weakly Lindelöf spaces, Proc. Amer. Math. Soc. 48 (1975), 454–457.

    Article  MathSciNet  Google Scholar 

  4. R. Engelking, General Topology, revised and completed edition, Heldermann Verlag (Berlin, 1989).

    MATH  Google Scholar 

  5. Lj. D. Kočinac, Some relative topological properties, Mat. Vesnik, 44 (1992), 33–44.

    MathSciNet  Google Scholar 

  6. C. M. Pareek, Hereditarily Lindelöf and hereditarily almost Lindelöf space, Math. Japonica, 30 (1985), 635–639.

    MATH  MathSciNet  Google Scholar 

  7. M. S. Sarsak, On relatively almost Lindelöf subsets, Acta Math. Hungar, 97 (2002), 109–114.

    Article  MATH  MathSciNet  Google Scholar 

  8. Yan-Kui Song, On relatively almost Lindelöf subsets, Acta Math. Hungar, 110 (2006), 213–220.

    Article  Google Scholar 

  9. M. Ulmer, Product of weakly α-compact spaces, Trans. Amer. Math. Soc., 170 (1972), 279–284.

    Article  MATH  MathSciNet  Google Scholar 

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The author acknowledges support from the NSFC (grant 10571081) and NSF of the Education Department of Jiangsu Province.

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Song, Y.K. On the product of relatively weakly almost Lindelöf subsets. Acta Math Hung 115, 315–318 (2007). https://doi.org/10.1007/s10474-007-5254-z

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  • DOI: https://doi.org/10.1007/s10474-007-5254-z

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