Siberian Mathematical Journal

, Volume 42, Issue 3, pp 465-472

First online:

Complemented Topologies on Abelian Groups

  • E. G. ZelenyukAffiliated withInstitute of Applied Problems of Mechanics and Mathematics
  • , I. V. ProtasovAffiliated withKiev National University

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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.