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1995 | 147 | 3 | 197-212
Tytuł artykułu

Large families of dense pseudocompact subgroups of compact groups

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EN
We prove that every nonmetrizable compact connected Abelian group G has a family H of size |G|, the maximal size possible, consisting of proper dense pseudocompact subgroups of G such that H ∩ H'={0} for distinct H,H' ∈ H. An easy example shows that connectedness of G is essential in the above result. In the general case we establish that every nonmetrizable compact Abelian group G has a family H of size |G| consisting of proper dense pseudocompact subgroups of G such that each intersection H H' of different members of H is nowhere dense in G. Some results in the non-Abelian case are also given.
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Twórcy
  • Department of Mathematics, Queens College, City University of New York, 65-30 Kissena Blvd., Flushing, New York 11367, U.S.A., zev@qcvaxa.acc.qc.edu
  • Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790, Japan
Bibliografia
  • [1] S. Balcerzyk and J. Mycielski, On the existence of free subgroups of topological groups, Fund. Math. 44 (1957), 303-308.
  • [2] T. Bröcker and T. Dieck, Representations of Compact Lie Groups, Springer, Berlin, 1985.
  • [3] W. W. Comfort, Some questions and answers in topological groups, in: Memorias del Seminario Especial de Topologia, vol. 5, Javier Bracho and Carlos Prieto (eds.), Instituto de Matemat. del'UNAM, México, 1983, 131-149.
  • [4] W. W. Comfort, On the "fragmentation" of certain pseudocompact groups, Bull. Greek Math. Soc. 25 (1984), 1-13.
  • [5] W. W. Comfort, Topological groups, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, Amsterdam, 1984, 1143-1263.
  • [6] W. W. Comfort, Some progress and problems in topological groups, in: General Topology and its Relations to Modern Analysis and Algebra VI, Proc. Sixth 1986 Prague Topological Symposium, Z. Frolík (ed.), Heldermann, Berlin, 1988, 95-108.
  • [7] W. W. Comfort and J. van Mill, Concerning connected pseudocompact Abelian groups, Topology Appl. 33 (1989), 21-45.
  • [8] W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Springer, Berlin, 1974.
  • [9] W. W. Comfort and L. C. Robertson, Extremal phenomena in certain classes of totally bounded groups, Dissertationes Math. 272 (1988).
  • [10] W. W. Comfort and K. A. Ross, Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966), 483-496.
  • [11] W. W. Comfort and T. Soundararajan, Pseudocompact group topologies and totally dense subgroups, ibid. 100 (1982), 61-84.
  • [12] D. Dikranjan, Zero-dimensionality of some pseudocompact groups, Proc. Amer. Math. Soc. 120 (1994), 1299-1308.
  • [13] R. Engelking, General Topology, Heldermann, Berlin, 1989.
  • [14] E. Hewitt, Rings of real-valued continuous functions, I, Trans. Amer. Math. Soc. 64 (1948), 45-99.
  • [15] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. I, Springer, Berlin, 1963.
  • [16] G. L. Itzkowitz, Extensions of Haar measure for compact connected Abelian groups, Indag. Math. 27 (1965), 190-207.
  • [17] G. Itzkowitz and D. Shakhmatov, Almost disjoint, dense pseudocompact subgroups of compact Abelian groups, in: Abstracts of Eighth Summer Conf. on General Topology and Applications (Queens College, CUNY, June 18-20, 1992), p. 37.
  • [18] G. Itzkowitz and D. Shakhmatov, Dense countably compact subgroups of compact groups, Math. Japon., to appear.
  • [19] G. Itzkowitz and D. Shakhmatov, Haar nonmeasurable partitions of compact groups, submitted.
  • [20] J. Price, Lie Groups and Compact Groups, London Math. Soc. Lecture Note Ser. 25, Cambridge Univ. Press, Cambridge, 1977.
  • [21] M. Rajagopalan and H. Subrahmanian, Dense subgroups of locally compact groups, Colloq. Math. 35 (1976), 289-292.
  • [22] D. Remus, Minimal and precompact group topologies on free groups, J. Pure Appl. Algebra 70 (1991), 147-157.
  • [23] N. Th. Varopoulos, A theorem on the continuity of homomorphisms of locally compact groups, Proc. Cambridge Philos. Soc. 60 (1964), 449-463.
  • [24] H. Wilcox, Pseudocompact groups, Pacific J. Math. 19 (1966), 365-379.
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Bibliografia
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