Vector Potentials in Simply Structured Spaces

The results obtained in a previous paper are extended from bounded to unbounded spaces. To do so, a new term, simply structured, is introduced. The result is as follows. In a simply structured space, whether it is bounded or unbounded, a piecewise smooth divergence-free vector function of position is the curl of another vector function of position called a vector potential. With this extension, it becomes clear why one can claim the existence of magnetic vector potentials. Magnetic induction is piecewise smooth and divergence-free in a simply structured space called the universe. Seven examples are presented to facilitate the understanding of the present discussion. They are about the electric and magnetic fields in infinite straight coaxial cables and the electric field in modified Euclidean spaces.