One-parameter subgroups of topological abelian groups

It is proved that, for a wide class of topological abelian groups (locally quasi-convex groups for which the canonical evaluation from the group into its Pontryagin bidual group is onto) the arc-component of the group is exactly the union of the one-parameter subgroups. We also prove that for metrizable separable locally arc-connected reflexive groups, the exponential map from the Lie algebra into the group is open.