Spaces of maps into topological group with the Whitney topology
Geometric Topology
2010-02-23 v2 General Topology
Abstract
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.
Cite
@article{arxiv.0904.1458,
title = {Spaces of maps into topological group with the Whitney topology},
author = {Taras Banakh and Kotaro Mine and Katsuro Sakai and Tatsuhiko Yagasaki},
journal= {arXiv preprint arXiv:0904.1458},
year = {2010}
}
Comments
11 pages