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On coverings in the lattice of all group topologies of arbitrary Abelian groups

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Abstract

The remainder of the completion of a topological abelian group (G, τ0) contains a nonzero element of prime order if and only if G admits a Hausdorff group topology τ1 that precedes the given topology and is such that (G, τ0) has no base of closed zero neighborhoods in (G, τ1).

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References

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Chişinau, Moldova

    V. I. Arnautov

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  1. V. I. Arnautov
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__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 5, pp. 961–973, September–October, 2006.

Original Russian Text Copyright © 2006 Arnautov V. I.

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Arnautov, V.I. On coverings in the lattice of all group topologies of arbitrary Abelian groups. Sib Math J 47, 787–796 (2006). https://doi.org/10.1007/s11202-006-0089-3

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  • DOI: https://doi.org/10.1007/s11202-006-0089-3

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