VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Division and ▫$k$▫-th root theorems for ▫$Q$▫-manifolds
    Banakh, Taras, 1968- ; Repovš, Dušan, 1954-
    We prove that a locally compact ANR-space ▫$X$▫ is a ▫$Q$▫-manifold if and only if it has the Disjoint Disk Property (DDP), all points of ▫$X$▫ are homological ▫$Z_\infty$▫-points and ▫$X$▫ has the ... countable-dimensional approximation property (cd-AP), which means that each map ▫$f: K \to X$▫ of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space ▫$X$▫ with DDP and cd-AP is a ▫$Q$▫-manifold if some finite power of ▫$X$▫ is a ▫$Q$▫-manifold. If some finite power of a space ▫$X$▫ with cd-AP is a ▫$Q$▫-manifold, then ▫$X^2$▫ and ▫$X \times [0,1]$▫ are ▫$Q$▫-manifolds as well. We construct a countable family ▫$\mathcal{X}$▫ of spaces with DDP and cd-AP such that no space ▫$X \in \mathcal{X}$▫ is homeomorphic to the Hilbert cube ▫$Q$▫ whereas the product ▫$X \times Y$▫ of any different spaces ▫$X, Y \in \mathcal{X}$▫ is homeomorphic to ▫$Q$▫. We also show that no uncountable family ▫$\mathcal{X}$▫ with such properties exists.
    Vir: Science in China. Series A, Mathematics. - ISSN 1006-9283 (Vol. 50, no. 3, 2007, str. 313-324)
    Vrsta gradiva - članek, sestavni del
    Leto - 2007
    Jezik - angleški
    COBISS.SI-ID - 14252121

    Povezava(-e):

    http://dx.doi.org/10.1007/s11425-007-0008-5

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