Connected LCA groups are sequentially connected (Q2856932)

The main result proved is that every connected locally compact group is sequentially connected, i.e., it cannot be split into two disjoint nonempty sequentially closed sets. The proof uses the Pontryagin-van Kampen duality of locally compact abelian groups.NEWLINENEWLINEThe above result is used to prove that if a Hausdorff topological group has a closed, sequentially connected subgroup which is feathered, i.e., \(H\) has a compact subgroup \(K\) such that \(H/K\) is metrizable, and if the quotient \(G/H\) is sequentially connected, then \(G\) is sequentially connected.NEWLINENEWLINEThe authors ask whether the main result remains valid for, in general, non-abelian groups. Several other open problems (conjectures) are formulated.