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  • Spaces of maps into topological group with the Whitney topology
    Banakh, 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 ▫$l_2$▫.
    Vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 157, no. 6, 2010, str. 1110-1117)
    Vrsta gradiva - članek, sestavni del
    Leto - 2010
    Jezik - angleški
    COBISS.SI-ID - 15502937

    Povezava(-e):

    http://dx.doi.org/10.1016/j.topol.2010.02.002

vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 157, no. 6, 2010, str. 1110-1117)

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