  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.
