Spaces of continuous maps from non-compact spaces into topological groups with the Whitney topology
Spaces of continuous maps from non-compact spaces into topological groups with the Whitney topology
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从非紧空间到惠特尼拓扑的拓扑群的连续映射空间
DOI：
10.1016/j.topol.2010.02.002
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发表时间：
2010
影响因子：
0.6
通讯作者：
and Tatsuhiko Yagasaki
中科院分区：
文献类型：
--
作者：
Taras Banakh;Kotaro Mine;Katsuro Sakai;and Tatsuhiko Yagasaki
设X是局部紧的Polish空间，G是非离散的Polish ANR群。用C（X，G）表示所有连续映射f：X→G的Whitney拓扑群，用Cc（X，G）表示所有具有紧支集的映射的子群。已知如果X是紧的且非离散的，则空间C（X，G）是l2-流形。本文证明了：若X是非紧的，且不是端离散的，则Cc（X，G）是（R∞×l2）-流形，且（C（X，G），Cc（X，G））局部同胚于l2的盒幂和小盒幂对.
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→G 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.