VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Detecting topological groups which are (locally) homeomorphic to LF-spaces
    Banakh, Taras, 1968- ...
    We prove that a topological group ▫$G$▫ is (locally) homeomorphic to an LF-spaceif ▫$G = \bigcup_{n \in \omega}G_n$▫ for some increasing sequence of subgroups ▫$(G_n)_{n \in \omega}$▫ such that: (1) ... for any neighborhoods ▫$U_n \subset G_n, \; n \in \omega$▫, of the neutral element ▫$e \in G_n \subset G$▫, the set ▫$\bigcup_{n=1}^\infty U_0U_1 \dots U_n$▫ is a neighborhood of ▫$e$▫ in ▫$G$▫; (2) each group ▫$G_n$▫ is (locally) homeomorphic to a Hilbert space; (3) for every ▫$n \in \mathbb{N}$▫ the quotient map ▫$G_n \to G_n/G_{n-1}$▫ is a locally trivial bundle; (4) for infinitely many numbers ▫$n \in \mathbb{N}$▫ each ▫$Z$▫-point in the quotient space ▫$G_n/G_{n-1} = \{xG_{n-1}: \; x \in G_n\}$▫ is a strong ▫$Z$▫-point.
    Vir: Fourth Workshop on Coverings, Selections and Games in Topology : on the occasion of Professor Ljubiša D. R. Kočinac's 65th birthday : special issue (Str. 2272-2284)
    Vrsta gradiva - prispevek na konferenci
    Leto - 2013
    Jezik - angleški
    COBISS.SI-ID - 16776793

    Povezava(-e):

    http://dx.doi.org/10.1016/j.topol.2013.07.023

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