Inverse limits of topological group cohomologies

Abstract:

For second countable locally compact almost connected groups $G$ and $A$, where $A$ is abelian and $G$ acts on $A$ continuously, it is shown that it is possible to represent $A$ as an inverse limit of Lie groups $\{ {A_n}\}$ compatible with the action of $G$ and such that ${H^{\ast }}(G,A)$ is isomorphic to ${\lim _n}\operatorname {inv} {H^{\ast }}(G,{A_n})$, provided that $A$ is compact or connected.