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LΣ(≤ ω)-spaces and spaces of continuous functions

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Central European Journal of Mathematics

Abstract

We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to \( \mathfrak{c} \) is an LΣ(≤ ω)-space.

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References

  1. Arhangel’skĭ A.V., Factorization theorems and function spaces: stability and monolithicity, Soviet Math. Dokl., 1982, 26(1), 177–181

    Google Scholar 

  2. Arhangel’skĭ A.V., Topological Function Spaces, Kluwer, Dordrecht, 1992

    Google Scholar 

  3. Casarrubias Segura F., Okunev O., Paniagua Ramírez C.G., Some results on LΣ(κ)-spaces, Comment. Math. Univ. Carolin., 2008, 49(4), 667–675

    MATH  MathSciNet  Google Scholar 

  4. Engelking R., On the double circumference of Alexandroff, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 1968, 16(8), 629–634

    MATH  MathSciNet  Google Scholar 

  5. Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989

    MATH  Google Scholar 

  6. Kubiś W., Okunev O., Szeptycki P.J., On some classes of Lindelöf Σ-spaces, Topology Appl., 2006, 153(14), 2574–2590

    Article  MATH  MathSciNet  Google Scholar 

  7. Nagami K., Σ-spaces, Fund. Math., 1969, 65, 169–192

    MATH  MathSciNet  Google Scholar 

  8. Okunev O., A method for constructing examples of M-equivalent spaces, Topology Appl. 1990, 36(2), 157–171, Correction: Topology Appl., 1993, 49(2), 191-192

    Article  MATH  MathSciNet  Google Scholar 

  9. Okunev O., On Lindelöf Σ-spaces of continuous functions in the pointwise topology, Topology Appl., 1993, 49(2), 149–166

    Article  MATH  MathSciNet  Google Scholar 

  10. Okunev O., Tamano K., Lindelöf powers and products of function spaces, Proc. Amer. Math. Soc., 1996, 124(9), 2905–2916

    Article  MATH  MathSciNet  Google Scholar 

  11. Simon P., On continuous image of Eberlein compacts, Comment. Math. Univ. Carolinae, 1976, 17(1), 179–194

    MATH  MathSciNet  Google Scholar 

  12. Sokolov G.A., On some classes of compact spaces lying in Σ-products, Comment. Math. Univ. Carolinae, 1984, 25(2), 219–231

    MATH  Google Scholar 

  13. Tkachuk V.V., A glance at compact spaces which map “nicely” onto the metrizable ones, Topology Proc., 1994, 19, 321–334

    MATH  MathSciNet  Google Scholar 

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Correspondence to Israel Molina Lara.

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Lara, I.M., Okunev, O. LΣ(≤ ω)-spaces and spaces of continuous functions. centr.eur.j.math. 8, 754–762 (2010). https://doi.org/10.2478/s11533-010-0039-y

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  • DOI: https://doi.org/10.2478/s11533-010-0039-y

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