FMF, Mathematical Library, Lj. (MAKLJ)
  • The topology of systems of hyperspaces determined by dimension functions
    Banakh, Taras, 1968- ; Mazurenko, Natalia
    Given a non-degenerate Peano continuum ▫$X$▫, a dimension function ▫$D \colon 2_\ast^X \to [0, \infty]$▫ defined on the family ▫$2_\ast^X$▫ of compact subsets of ▫$X$▫, and a subset ▫$\Gamma \subset ... [0,\infty)$▫, we recognize the topological structure of the system ▫$\langle 2^X, D_{\le \gamma}(X) \rangle_{\alpha \in \Gamma}$▫, where ▫$2^X$▫ is the hyperspace of non-empty compact subsets of ▫$X$▫ and ▫$D_{\le \gamma}(X)$▫ is the subspace of ▫$2^X$▫, consisting of non-empty compact subsets ▫$K \subset X$▫ with ▫$D(K) \le \gamma$▫.
    Source: Proceedings of the Infinite Dimensional Analysis and Topology (IDAT) Conference 2009 (Str. 43-53)
    Type of material - conference contribution
    Publish date - 2009
    Language - english
    COBISS.SI-ID - 15522393

    Link(s):

    http://dx.doi.org/10.1016/j.top.2009.11.002

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