VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • The diffeomorphism groups of the real line are pairwise bihomeomorphic
    Banakh, Taras, 1968- ; Yagasaki, Tatsuhiko
    For an ▫$r = 0,1,...,\infty$▫, by ▫${\mathcal D}^r (\mathbb{R})$▫, ▫${\mathcal D}_+^r (\mathbb{R})$▫, ▫${\mathcal D}_c^r (\mathbb{R})$▫ we denote respectively the groups of ▫$C^r$▫ diffeomorphisms, ... orientation-preserving ▫$C^r$▫ diffeomorphisms, and compactly supported ▫$C^r$▫ diffeomorphisms of the real line. We think of these groups as bitopologies spaces endowed with the compact-open ▫$C^r$▫ topology and the Whitney ▫$C^r$▫ topology. We prove that allthe triples , ▫$({\mathcal D}^r ({\mathbb{R}}), {\mathcal D}_+^r ({\mathbb{R}}), {\mathcal D}_c^r ({\mathbb{R}})) \le r \le \infty$▫, are pairwise bitopologically equivalent, which allows us to apply known results on the topological structure of homeomorphism groups of the real line to recognizing the topological structure of the diffeomorphism groups of ▫$\mathbb{R}$▫.
    Vir: Proceedings of the Infinite Dimensional Analysis and Topology (IDAT) Conference 2009 (Str. 119-129)
    Vrsta gradiva - prispevek na konferenci
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 15522649

    Povezava(-e):

    http://dx.doi.org/10.1016/j.top.2009.11.010

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