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Let X be a locally compact Polish space and G a non-discrete Polish ANRgroup. By C(X,G), we denote the topological group of all continuous maps f:X\to G endowed with the Whitney (graph) topology and by C_c(X,G) the subgroupconsisting of all maps with compact support. It is known that if X is compactand non-discrete then the space C(X,G) is an l_2-manifold. In this article weshow that if X is non-compact and not end-discrete then C_c(X,G) is an(R^\infty \times l_2)-manifold, and moreover the pair (C(X,G), C_c(X,G)) islocally homeomorphic to the pair of the box and the small box powers of l_2.

Spaces of maps into topological group with the Whitney topology