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10.6 (1986)

Solved

Is it true that in an abelian group every non-discrete group topology can be strengthened up to a non-discrete group topology such that the group becomes a complete topological group?

Contributor: V. I. Arnautov

Progress

This is true for group topologies satisfying the first axiom of countability (E. I. Marin, in: Modules, Algebras, Topologies (Mat. Issledovaniya, 105), Kishinev, 1988, 105–119 (Russian)), but this may not be true in general, see Problem 12.2.

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