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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
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