Spaces of maps into topological group with the Whitney topology

Details Spaces of maps into topological group with the Whitney topology Spaces of maps into topological group with the Whitney topology

2009-04-09

arxiv.org/abs/0904.1458v2

Topology Appl., 157 (2010) 1110 - 1117

Mathematics

Geometric Topology

11 pages

Scientific paper

Let X be a locally compact Polish space and G a non-discrete Polish ANR group. 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 subgroup consisting of all maps with compact support. It is known that if X is compact and non-discrete then the space C(X,G) is an l_2-manifold. In this article we show 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)) is locally homeomorphic to the pair of the box and the small box powers of l_2.

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