  It is suggested that the original, minimal Kaluza-Klein theory should be
extended by adding a 5-dimensional version of the Gibbons-Hawking gravitational
surface term. It is then demonstrated that the usual dimensional reduction of
the newly added surface (boundary) term leads to the emergence of the famous
Abelian Chern-Simons term. It is stressed that the advent of this Chern-Simons
term is not merely a parametrization artefact but a real thing. Finally, the
issue of finite-ranged electromagnetic interaction due to massive photons on a
plane has been interpreted in terms of the violation of the local gauge
invariance of this extended version of Kaluza-Klein theory.
