  We construct a universal continuous invariant bilinear form for the Lie
algebra of compactly supported sections of a Lie algebra bundle in a
topological sense. Moreover we construct a universal continuous central
extension of a current algebra that is the tensor product of a
finite-dimensional Lie algebra g and a certain topological algebra A. In
particular taking A as the compactly supported smooth functions on a
sigma-compact manifold M, we obtain a more detailed justification for a recent
result of Janssens and Wockel concerning a universal extension for the Lie
algebra of compactly supported g-valued smooth functions on M.
