Abstract
In the background of a Robertson-Walker universe model with a positive spatial curvature and arbitrary time evolution, the exact solution of a sourceless magnetic field with finite range is presented. The field seems an inhomogeneous solid torus spanning the entire space, and is nonsingular. Both topologies that permit global isotropy are considered: the three-sphere ${\mathbf{S}}^{3}$ and the multiply connected projective three-space ${\mathbf{P}}^{3}$.
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