Spaces of maps into topological group with the Whitney topology

Autor:	Banakh, Taras, Mine, Kotaro, Sakai, Katsuro, Yagasaki, Tatsuhiko
Rok vydání:	2009
Předmět:	Mathematics - Geometric Topology Mathematics - General Topology 46A13 46T10 54H11 57N20 58D15
Zdroj:	Topology Appl., 157 (2010) 1110 - 1117
Druh dokumentu:	Working Paper
Popis:	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. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0904.1458 Zobrazit plný text záznamu View this record from Arxiv