Spaces of maps into topological group with the Whitney topology

作者：Banakh Taras; Mine Kotaro; Sakai Katsuro; Yagasaki Tatsuhiko^*

来源：Topology and Its Applications, 2010, 157(6): 1110-1117.

DOI：10.1016/j.topo1.2010.02.002

• Frechet space
• LF-space
• Topological group
• I(2)-manifold
• (R(infinity) x I(2))-manifold
• Function space
• The Whitney (graph) topology
• The box product
• The small box product
• End-discrete

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 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 I(2)-manifold. In this article we show that if X is non-compact and not end-discrete then C(c)(X, G) is an

• 出版日期2010-4-15