  We give a criterion for a group homomorphism on a valued abelian group to be
surjective and to preserve spherical completeness. We apply this to give a
criterion for the existence of integration on a valued differential field.
Further, we give a criterion for a sum of spherically complete subgroups of a
valued abelian group to be spherically complete. This in turn can be used to
determine elementary properties of power series fields in positive
characteristic.
