Abstract:We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if $H$ is a connected locally compact Abelian subgroup of a Hausdorff topological group $G$ and the quotient space $G/H$ is sequentially connected, then so is $G$.
Keywords: locally compact, connected, sequentially connected, Pontryagin duality, torsion-free, divisible, metrizable element, extension of a group
AMS Subject Classification: 22A30 54H10 54D30 54A25