This article is cited in 2 papers

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

V. I. Arnautov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Abstract: The remainder of the completion of a topological abelian group $(G,\tau_0)$ contains a nonzero element of prime order if and only if $G$ admits a Hausdorff group topology $\tau_1$ that precedes the given topology and is such that $(G,\tau_0)$ has no base of closed zero neighborhoods in $(G,\tau_1)$.

Keywords: abelian group, group topology, lattice of topologies, covering, preceding topology, completion.

UDC: 512.546.2

Received: 09.03.2005

 English version: Siberian Mathematical Journal, 2006, 47:5, 787–796

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