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Spaces of maps into topological group with the Whitney topologyBanakh, Taras, 1968- ...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 ▫$f\colon X \to G$▫ 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 ▫$(\mathbb R {\mathbb R}^\infty \times l_2)$▫-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 ▫$l_2$▫.Source: Topology and its Applications. - ISSN 0166-8641 (Vol. 157, no. 6, 2010, str. 1110-1117)Type of material - article, component partPublish date - 2010Language - englishCOBISS.SI-ID - 15502937
Author
Banakh, Taras, 1968- |
Mine, Kotaro |
Sakai, Katsuro |
Yagasaki, Tatsuhiko
Topics
matematika |
funkcionalna analiza |
topologija |
Fréchetov prostor |
LF-prostor |
topološka grupa |
▫$l_2$▫-mnogoterost |
▫$({\mathbb R}^\infty \times l_2)$▫-mnogoterost |
funkcijski prostor |
mathematics |
functional analysis |
topology |
Fréchet space |
LF-space |
topological group |
▫$l_2$▫-manifold |
▫$({\mathbb R}^\infty \times l_2)$▫-manifold |
function space |
Whitney (graph) topology |
box product |
small box product |
end-discrete
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Banakh, Taras, 1968- | 31193 |
Mine, Kotaro | ![]() |
Sakai, Katsuro | ![]() |
Yagasaki, Tatsuhiko | ![]() |
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