Siberian Mathematical Journal

, Volume 42, Issue 3, pp 465–472 | Cite as

Complemented Topologies on Abelian Groups

  • E. G. Zelenyuk
  • I. V. Protasov


A topology τ on a group G is complemented if there exists an indiscrete topology τ' on G such that UV={0} for suitable neighborhoods of zero U and V in the topologies τ and τ. The authors give a complementation test for an arbitrary topology. Locally compact groups with complemented topologies have been described. A group all of whose continuous homomorphic images are complete is proved to be compact. A family of 2ω topologies that are pairwise complementary to one another is defined for an arbitrary group.


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  1. 1.
    Zelenyuk E. G. and Protasov I. V., “Topology on Abelian groups,” Izv. Akad. Nauk SSSR Ser. Mat., 54, No. 5, 1090–1107 (1990).Google Scholar
  2. 2.
    Protasov I. V. and Zelenuk E. G., “Topologies on Z determined by sequences: seven open problems,” Mat. Stud., 12, No. 1, 111 (1999).Google Scholar
  3. 3.
    Protasov I. V., “Decomposition of groups,” Mat. Stud., 9, No. 2, 130–148 (1998).Google Scholar
  4. 4.
    Greenleaf F. P., Invariant Means on Topological Groups and Their Applications [Russian translation], Mir, Moscow (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • E. G. Zelenyuk
    • 1
  • I. V. Protasov
    • 2
  1. 1.Institute of Applied Problems of Mechanics and MathematicsL'vovUkraine
  2. 2.Kiev National UniversityKievUkraine

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