Arnautov, V. I. On coverings in the lattice of all group topologies of arbitrary Abelian groups. (Russian, English) Zbl 1150.54347 Sib. Mat. Zh. 47, No. 5, 961-973 (2006); translation in Sib. Math. J. 47, No. 5, 787-796 (2006). Summary: 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 \((G,\tau_1)\). MSC: 54H11 Topological groups (topological aspects) 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 22A05 Structure of general topological groups 06B30 Topological lattices Keywords:lattice of topologies; preceding topology; completion PDF BibTeX XML Cite \textit{V. I. Arnautov}, Sib. Mat. Zh. 47, No. 5, 961--973 (2006; Zbl 1150.54347); translation in Sib. Math. J. 47, No. 5, 787--796 (2006) Full Text: EMIS EuDML