Polish LCA groups are strongly characterizable

Positively answering a question of Gabriyelyan [21, Problem 2.13], we prove that for every second countable locally compact abelian group G and every continuous monomorphism s : G → K into a compact metrizable abelian group K, there exists a sequence of characters ( u n ) of K characterizing the subgroup s ( G ) , i.e., s ( G ) coincides with the subset of those elements k ∈ K such that ( u n ( k ) ) is a null-sequence in the circle group T .