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Hyperstonean cover and second dual extension

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References

  1. J. Wada, Stonian spaces and the second conjugate spaces of AM-spaces,Osaka Math. J.,9 (1957), 195–200.

    Google Scholar 

  2. S. Kaplan, On the second dual of the space of continuous functions I, II, III, IV,Trans. Amer. Math. Soc.,I 86 (1957), 70–90;II 93 (1957), 329–350; III101 (1961), 34–51; IV113 (1964), 512–546.

    Google Scholar 

  3. J. Mach, The order dual of the space of Radon measures,Trans. Amer. Math. Soc.,113 (1964) 219–239.

    Google Scholar 

  4. Z. Semadeni, Spaces of continuous functions on compact sets,Advanc. Math.,1 (1965), 319–382.

    Google Scholar 

  5. H. Gordon, The maximal ideal space of a ring of measurable functions,Amer. J. Math.,88 (1966), 827–843.

    Google Scholar 

  6. S. Kaplan, The unbounded bidual ofC(X), Ill.J. Math.,17 (1973), 619–645.

    Google Scholar 

  7. C. Shannon, The second dual ofC(X), Pacif. J. Math.,72 (1977), 237–253.

    Google Scholar 

  8. D. Sentilles, AnL 1-space for Boolean algebras and semi-reflexivity of spacesL (X, Σ, μ),Trans. Amer. Math. Soc.,226 (1977), 1–37.

    Google Scholar 

  9. W. H. Graves, On the theory of vector measures,Mem. Amer. Math. Soc.,195 (1977).

  10. W. H. Graves, D. Sentilles, The extension and completion of the universal measure and the dual of the space of measures,J. Math. Anal. Appl.,68 (1979), 228–264.

    Google Scholar 

  11. C. Constantinescu,Duality in measure theory, Lecture Notes in Math., 796, Springer-Verlag (Berlin, 1980).

    Google Scholar 

  12. M. Cambern, P. Greim, The bidual ofC(X, E), Proc. Amer. Math. Soc.,85 (1982), 53–58.

    Google Scholar 

  13. C. H. Brook, On the universal measure space,J. Math. Anal. Appl.,85 (1982), 584–598.

    Google Scholar 

  14. Б. З. Вулих, Определе ние произведения в ли нейном полуупорядоч енном пространствеДАН СССР,26 (1940), 847–851.

    Google Scholar 

  15. S. Kakutani, Concrete representation of abstractM-spaces (A characterization of the space of continuous functions),Ann. Math.,42 (1941), 994–1024.

    Google Scholar 

  16. R. F. Arens, Operations induced in functional classes,Monatsh. Math.,55 (1951), 1–19.

    Google Scholar 

  17. A. Grothendieck, Un résultat sur le dual d'uneC *-algèbre,J. Math. Pures Appl.,36 (1957), 97–108.

    Google Scholar 

  18. D. A. Edwards, A class of topological Boolean algebras,Proc. London Math. Soc.,13 (1963), 413–429.

    Google Scholar 

  19. S. P. Lloyd, A mixing condition for extreme left invariant means,Trans. Amer. Math. Soc.,125 (1966), 461–481.

    Google Scholar 

  20. G. L. Seever, Nonnegative projections onC 0(X),Pacif. J. Math.,17 (1966), 159–166.

    Google Scholar 

  21. J. Flachsmeyer, Topologization of Boolean algebras,General Topology and its Relations to Modern Analysis and Algebra IV (Prague, 1976), Lecture Notes in Math.,609 (1977), 81–97.

    Google Scholar 

  22. V. Zaharov, Characterization of the hyperstonean cover of a compact,Proc. Conf. Topology and Measure III (Vitte, GDR, 1980), Greifswald, 1982, 357–359.

    Google Scholar 

  23. В. К. Захаров, Харак теризация гиперзтоу нова накрытия компак та,Функц. анализ и его прилож.,15 (1981), 79–80.

    Google Scholar 

  24. V. Zaharov, On the hyperstonian cover of a compact,Math. Nachr.,107 (1982), 175–186.

    Google Scholar 

  25. V. Zaharov, Topological and algebraical aspects of some sets of measurable functions,General Topology and its Relations to Modern Analysis and Algebra V (Prage, 1981), “Heldermann Verlag”, Berlin, 1982, 706–712.

    Google Scholar 

  26. В. К. Захаров, Гипер стоунов абсолют впол не регулярного прост ранства,ДАН СССР,267 (1982), 280–283.

    Google Scholar 

  27. V. K. Zaharov, On hyperstonean absolute and Borel cover,Тезисы Л енинградской междун. тополог, конф., Наука (Ленинград, 1982), 169.

    Google Scholar 

  28. V. K. Zaharov, Topological characterization of the hyperstonean cover,Proc. Topol. Conf. Leningrad, 1982), Lecture Notes in Math.,1060 (1984), 115–118.

    Google Scholar 

  29. V. K. Zaharov, Some perfect preimages connected with extensions of the family of continuous functions,Topology Theory and Appl., Proceedings of the Topological Conference (Eger, Hungary, 1983), J. Bolyai Math. Soc. - North Holland, 1985.

    Google Scholar 

  30. В. К. Захаров, О двух классических расшир ениях векторной реше тки непрерывных функ ций,Функц. анализ и ег о прилож.,18 (1984), 92–93.

    Google Scholar 

  31. А. В. Архангельский, В. И. Пономарев,Осно вы общей топологии в з адачах и упражнениях, Наука (Москва, 1974).

    Google Scholar 

  32. J. Lambek,Lectures on rings and modules, Blaisdell Publishing Company (Toronto, 1966).

    Google Scholar 

  33. L. Fuchs,Partially ordered algebraic systems, Pergamon Press (Oxford, 1963).

    Google Scholar 

  34. N. Bourbaki,Intégration, Hermann (Paris, 1963).

    Google Scholar 

  35. Z. Semadeni,Banach spaces of continuous functions, Polish Scientific Publishers (Warszawa, 1971).

    Google Scholar 

  36. W. A. J. Luxemburg, A. C. Zaanen,Riesz spaces, North-Holland Publishing Company (Amsterdam, 1971).

    Google Scholar 

  37. R. Sikorski,Boolean algebras, Springer-Verag (Berlin, 1964).

    Google Scholar 

  38. J. L. Kelley, Measures in Boolean algebras,Pacif. J. Math.,9 (1959), 1165–1177.

    Google Scholar 

  39. J. -P. Delfosse, Caractérisations d'anneaux de fonctions continues,Ann. Soc. Sci. Bruxelles, sér. I,89 (1975), 364–368.

    Google Scholar 

  40. K. Kuratowski,Topology, v.l, Academic Press (New York-London, 1966).

    Google Scholar 

  41. V. K. Zaharov, A. B. Koldunov, Characterization of theσ-cover of a compact,Math. Nachr.,107 (1982), 7–16.

    Google Scholar 

  42. E. Hewitt, K. Stromberg,Real and abstract analysis, Springer-Verlag (Berlin, 1965).

    Google Scholar 

  43. Y. Mibu, Relations between measure and topology in some Boolean spaces,Proc. Imp. Acad. Toko,20 (1944), 454–558.

    Google Scholar 

  44. J. B. Cooper,Saks spaces and applications to functional analysis, North-Holland Publishing Company (Amsterdam, 1978).

    Google Scholar 

  45. Б. З.Вулих,Введение в теорию полуупорядоч енных пространств, Го с. изд. физ.-мат. лит; (Моск ва, 1961).

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Zaharov, V.K. Hyperstonean cover and second dual extension. Acta Math Hung 51, 125–149 (1988). https://doi.org/10.1007/BF01903626

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  • DOI: https://doi.org/10.1007/BF01903626

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