Eine Spektralsequenz in der stetigen Kohomologietheorie topologischer Gruppen

Let H^*(G; M) be the continuous cohomology of a locally compact group G with coefficients in a topological RG-module M. If G operates without fixed points on a R-paracompact space X such that there is a slice through each point and X/G is R-paracompact, then there exists a spectral sequence converging to the equivariant cohomology H^*(X,G; M) of X with second term E₂ ^p.q?H^p(G; H^qX; M)) where the sheaf theoretical cohomology of X is suitable topologized. Several applications and a generalization to actions of G with non-empty fixed point sets are given.