## Algebraic cohomology of topological groups |

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a-compact abelian groups abelian topological groups abstract G-modules abstract group algebraic cohomology Buchsbaum's criterion c-space closed subgroup cohomology groups Coker cokernel compact set complete metric abelian complete metric G-modules complete subcategory continuous cochains continuous map Corollary countable define definition Diagram Q differentiable G-module double complex exact connected sequence Exti(Z faces and degeneracies fibration finite dimensional function G-vector group G group ring Hence Hochschild and Mostow homotopy lifting property identity induced integrable isomorphic Let h Lie algebra Lie group locally compact locally contractible long exact sequence Markov topology metric abelian topological modules natural transformation O-dimensional paracompact Proof proper exact rows proper exact sequences property F Proposition Bl pseudometrizable quasi-abelian S-category quotient retractive sequence of functors sequence of topological sheaf of germs short exact sequence spectral sequence subspace of F(G surjective Theorem topological G-module topological spaces topological vector space topology with respect weak topology weakly separable group