(UL)
  • Closed locally path-connected subspaces of finite-dimensional groups are locally compact
    Banakh, Taras, 1968- ; Zdomskyy, Lyubomyr, 1983-
    We prove that each closed locally continuum-connected subspace of a finite dimensional topological group is locally compact. This allows us to construct many 1-dimensional metrizable separable spaces ... that are not homeomorphic to closed subsets of finite-dimensional topological groups, which answers in the negative a question of Dmitrii Shakhmatov. Another corollary is a characterization of Lie groups as finite-dimensional locally continuum-connected topological groups. For locally path connected topological groups this characterization was proved by Andrew M. Gleason and Richard S. Palais in 1957.
    Vir: Topology proceedings. - ISSN 0146-4124 (Vol. 36, 2010, str. 399-405)
    Vrsta gradiva - članek, sestavni del
    Leto - 2010
    Jezik - angleški
    COBISS.SI-ID - 15668057

    Povezava(-e):

    http://topology.auburn.edu/tp/restricted/v36/tp36027.pdf

vir: Topology proceedings. - ISSN 0146-4124 (Vol. 36, 2010, str. 399-405)

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