Siberian Mathematical Journal

, Volume 42, Issue 3, pp 465–472

Complemented Topologies on Abelian Groups

  • E. G. Zelenyuk
  • I. V. Protasov

DOI: 10.1023/A:1010466924961

Cite this article as:
Zelenyuk, E.G. & Protasov, I.V. Siberian Mathematical Journal (2001) 42: 465. doi:10.1023/A:1010466924961


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.

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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