  E. C. Zeeman [1] has criticized the fact that in all articles and books until
that moment (1967) the topology employed to work with the Minkowski space was
the Euclidean one. He has proposed a new topology, which was generalized for
more general space-times by Goebel [2]. In the Zeeman and Goebel topologies for
the space-time, the unique continuous curves are polygonals composed by
time-like straight lines and geodesics respectively. In his paper, Goebel
proposes a topology for which the continuous curves are polygonals composed by
motions of charged particles. Here we obtain in a very simple way a
generalization of this topology, valid for any gauge fields, by employing the
projection theorem of Kaluza-Klein theories (page 144 of Bleecker [3]). This
approach relates Zeeman topologies and Kaluza-Klein, therefore Gauge Theories,
what brings insights and points in the direction of a completely geometric
theory.
