  Conditions for the appearance of topological charges are studied in the
framework of the universal C*-algebra of the electromagnetic field, which is
represented in any theory describing electromagnetism. It is shown that
non-trivial topological charges, described by pairs of fields localised in
certain topologically non-trivial spacelike separated regions, can appear in
regular representations of the algebra only if the fields depend non-linearly
on the mollifying test functions. On the other hand, examples of regular vacuum
representations with non-trivial topological charges are constructed, where the
underlying field still satisfies a weakened form of "spacelike linearity". Such
representations also appear in the presence of electric currents. The status of
topological charges in theories with several types of electromagnetic fields,
which appear in the short distance (scaling) limit of asymptotically free
non-abelian gauge theories, is also briefly discussed.
