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Compact and compactly generated groups

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References for Chapter III

  1. P. R. Halmos, Measure Theory, Van Nostrand, 1950.

    Google Scholar 

  2. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer-Verlag, 1963.

    Google Scholar 

  3. E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer-Verlag, 1975.

    Google Scholar 

  4. W. W. Comfort, K. H. Hofmann, D. Remus, Topological groups and semigroups, Recent Progress in Topology (M. Husek and J. van Mill, eds.), Elsevier Sci. Publ., 1992, pp. 57–144.

    Google Scholar 

  5. W. W. Comport and N. Negrepontis, Chain Conditions in Topology, Cambridge Univ. Press, 1982.

    Google Scholar 

  6. M. G. Tkachenko, On topologies of free groups, Czech. Math. J. 34 (109) (1984), 541–551.

    MathSciNet  MATH  Google Scholar 

  7. V. G. Pestov, Compactly generated topological groups, Math. Notes 40 (1986), 880–882.

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Haydon, On a problem of Pelczynski, Studia Math., 52 (1974), 23–31.

    MathSciNet  MATH  Google Scholar 

  9. E. V. Schepin, Functors and uncountable powers of compacta, Russian Math. Surveys 36 (3) (1981), 1–71.

    Article  Google Scholar 

  10. V.V. Uspenskiî, Why compact groups are dyadic, Proceedings of the Sixth Prague Topological Symposium 1986, Heldermann Verlag, Berlin, 1988, pp. 601–610.

    Google Scholar 

  11. V.V. Uspenskii, Topological groups and Dugundji compact spaces, Math. USSR Sbornik 67 (2) (1990), 555–580.

    Article  MathSciNet  Google Scholar 

  12. E. Michael, Selected selection theorems, Amer. Math. Monthly 58 (1956), 233–238.

    Article  MathSciNet  MATH  Google Scholar 

  13. C. Bessaga and A. Pelczynski, Selected topics in infinite-dimensional topology, PWN Warszaw, 1975.

    MATH  Google Scholar 

  14. V.V. Fedorchuk and V.V. Filipov, General topology. Basic constructions, Moscow State University Press, 1988 (in Russian).

    Google Scholar 

  15. J.L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165–1177.

    Article  MathSciNet  MATH  Google Scholar 

  16. J.L. Kelley, Topology, D. Van Nostrand Company, In., Princeton, 1955.

    MATH  Google Scholar 

  17. E. Michael, Continuous selections I, II, III, Ann. of Math. 63 (1956), 361–382; 64 (1956), 362–580; 65 (1957), 375–390.

    Article  MathSciNet  MATH  Google Scholar 

  18. T.N. Herstein, Topics in algebra, John Wiley & Sons, New York, 1975.

    MATH  Google Scholar 

  19. D. Montgomeri and L. Zippin, Topological transformation groups, R.E. Krieger Publ. Co., New York, 1974.

    Google Scholar 

  20. A.A. Markov, On free topological groups, Doklady Akad. Nauk SSSR 31 (1941), 299–301.

    MathSciNet  Google Scholar 

  21. M.I. Graev, Free topological group, Translations Series 1, Vol 8 (1962), American Mathematical Society, Providence, 30-5-364.

    Google Scholar 

  22. A.V. Arhangel'skiî, Algebraic objects generated by topological structure, J. Soviet Mathematics 45 (1989), 141–198.

    MathSciNet  Google Scholar 

  23. W.W. Comfort, Problems on topological groups and other topological spaces, Open Problems in Topology (J. van Mill and G.M. Reid, eds.), Elsevier Sci. Publ., 1990, pp. 313–347.

    Google Scholar 

  24. J. Cleary and S.A. Morris, Locally dyadic topological groups. Bull. Austr. Math. Soc. 40 (1989), 417–419.

    Article  MathSciNet  MATH  Google Scholar 

  25. I. Guran, On topological groups close to being Lindelöf, Soviet Math. Dokl. 23 (1981), 173–175.

    MATH  Google Scholar 

  26. G. Hochschild, The structure of Lie groups, Holder-Day, San Francisco, 1965.

    MATH  Google Scholar 

  27. S.A. Morris, Locally compact topological Abelian groups, Math. Proc. Cambridge Phil. Soc. 101 (1987), 233–235.

    Article  Google Scholar 

  28. B.A. Pasynkov, On spaces with a compact group of transformations, Soviet Math. Dokl. 17 (1976), 1522–1526.

    MATH  Google Scholar 

  29. V. Pestov, Some properties of free topological groups, Moscow Univ. Math. Bull. 37 (1982), 46–49.

    MathSciNet  MATH  Google Scholar 

  30. L.S. Pontryagin, Topological groups, Princeton Univ. Press, Princeton, 1939.

    MATH  Google Scholar 

  31. D.B. Shakhmatov, A problem of coincidence of dimension in topological group, Topology Appl. 33 (1989), 105–113.

    Article  MathSciNet  MATH  Google Scholar 

  32. D.B. Shakhmatov, Precalibres of σ-compact topological groups, Math. Notes 39 (1986), 465–470.

    Article  MathSciNet  MATH  Google Scholar 

  33. M.G. Tkachenko, The Souslin property of free topological groups on bicompacta, Math. Notes 34 (1983), 750–793.

    Article  MathSciNet  Google Scholar 

  34. D.B. Shakhmatov, Dugundji spaces and topological groups, Comm. Math. Univ. Carolinae 31 (1990), 127–143.

    MathSciNet  MATH  Google Scholar 

  35. S. Todorcevic, Some applications of S and L combinatorics, Annals of the New York Academy of Sciences, Vol. 705, 130–167.

    Google Scholar 

  36. V.V. Uspenskiî, Topological groups and Dugundji compacta, Math. USSR Sbornik 67 (1990), 555–580.

    Article  MATH  Google Scholar 

  37. V.V. Uspenskiî, Compact factor spaces of topological groups and Haydon spectra, Math. Notes 42 (1987), 827–831.

    Article  Google Scholar 

  38. V.V. Tkachuk, On a method of construction examples of m-equivalent spaces, Russian Math. Surveys 38 (1983), 135–136.

    Article  MathSciNet  MATH  Google Scholar 

  39. A.G. Kurosh, The theory of groups, Vols I and II, Chelsea Publ. Co. New York, 1960.

    Google Scholar 

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Todorcevic, S. (1997). Compact and compactly generated groups. In: Topics in Topology. Lecture Notes in Mathematics, vol 1652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096298

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  • DOI: https://doi.org/10.1007/BFb0096298

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