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Tytuł artykułu

Group reflection and precompact paratopological groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We construct a precompact completely regular paratopological Abelian group G of size (2ω)+ such that all subsets of G of cardinality ≤ 2ω are closed. This shows that Protasov’s theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups. We also prove that the group reflection of the product of an arbitrary family of paratopological (even semitopological) groups is topologically isomorphic to the product of the group reflections of the factors, and that the group reflection, H*, of a dense subgroup G of a paratopological group G is topologically isomorphic to a subgroup of G*.
Wydawca
Rocznik
Tom
1
Strony
22-30
Opis fizyczny
Daty
otrzymano
2012-12-10
zaakceptowano
2013-03-20
online
2013-07-16
Twórcy
  • Departamento de Matemáticas, Universidad Autónoma Metropolitana
    Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa C.P. 09340,
    México, D.F., Mexico, mich@xanum.uam.mx
Bibliografia
  • [1] A. V. Arhangel’skii and M. G. Tkachenko, Topological Groups and Related Structures, Atlantis Series in Mathematics,vol. I, Atlantis Press and World Scientific, Paris–Amsterdam 2008.
  • [2] T. Banakh and O. Ravsky, Oscillator topologies on a paratopological group and related number invariants, AlgebraicStructures and their Applications, Kyiv: Inst. Mat. NANU, (2002), 140-152.
  • [3] W.W. Comfort, and K. A. Ross, Pseudocompactness and uniform continuity in topological groups, Pacific J. Math.16 (1966), 483–496.
  • [4] S. Dierolf and U. Schwanengel, Examples of locally compact non-compact minimal topological groups, Pacific J.Math. 82 (1979), 349–355.
  • [5] R. Engelking, General Topology, Heldermann Verlag, Berlin 1989.
  • [6] M. Fernández, On some classes of paratopological groups, Topology Proc. 40 (2012), 63–72.
  • [7] L. S. Pontryagin, Continuous groups, third edition, “Nauka”, Moscow 1973.
  • [8] I. V. Protasov, Discrete subsets of topological groups, Math. Notes 55 (1994) no. 1–2, 101–102. Russian originalin: Mat. Zametki 55 (1994), 150–151.
  • [9] O. V. Ravsky, Paratopological groups, II, Mat. Studii 17 (2002), no. 1, 93–101.[WoS]
  • [10] M. G. Tkachenko, Paratopological Groups: Some Questions and Problems, Q&A in General Topology 27 no. 1(2009), 1–21.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_taa-2013-0003
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