Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 16 Accesses

  • 1 Citations

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).

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Arnautov V. I. and Filippov K. M., “On premaximal topologies on vector spaces,” Bul. Acad. Ştiinţ. Republicii Moldova Mat., 1, No. 20, 96–105 (1996).

  2. 2.

    Arnautov V. I. and Filippov K. M., “On maximal chains in the lattice of module topologies,” Siberian Math. J., 42, No. 3, 415–427 (1999).

  3. 3.

    Arnautov V. I. and Filippov K. M., “On coverings in the lattice of linear topologies,” Bul. Acad. Ştiinţ. Republicii Moldova Mat., 2, No. 30, 7–16 (1999).

  4. 4.

    Arnautov V. I. and Filippov K. M., “On coverings in the lattice on a group of finite period, ” Bul. Acad. Ştiinţ. Republicii Moldova Mat., 2, 77–87 (2002).

  5. 5.

    Arnautov V. I., Glavatsky S. T., and Michalev A. V., Introduction to the Theory of Topological Rings and Modules, Marcel Dekker Inc., New York; Basel; Hong Kong (1996).

  6. 6.

    Dikranjan D. N., Prodanov I. R., and Stoyanov L. N., Topological Groups, Marcel Dekker Inc., New York; Basel (1989).

Download references

Author information

Additional information

__________

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

Original Russian Text Copyright © 2006 Arnautov V. I.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Keywords

  • abelian group
  • group topology
  • lattice of topologies
  • covering
  • preceding topology
  • completion