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Spaces of maps into topological group with the Whitney topology |
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| Authors: | Taras Banakh Kotaro Mine |
| Institution: | a Instytut Matematyki, Uniwersytet Humanistyczno-Przyrodniczy Jana Kochanowskiego w Kielcach, Poland b Department of Mathematics, Ivan Franko National University of Lviv, Lviv 79000, Ukraine c Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan d Division of Mathematics, Kyoto Institute of Technology, Kyoto 606-8585, Japan |
| 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  endowed with the Whitney (graph) topology and by Cc(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 l2-manifold. In this article we show that if X is non-compact and not end-discrete then Cc(X,G) is an (R∞×l2)-manifold, and moreover the pair (C(X,G),Cc(X,G)) is locally homeomorphic to the pair of the box and the small box powers of l2. |
| Keywords: | 46A13 46T10 54H11 57N20 58D15 |
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