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  • A universal model infinite-dimensional space
    Banakh, Taras, 1968- ; Shabat, Oryslava ; Zarichnyi, Michael, 1958-
    Given an ordinal ▫$\alpha$▫ and a pointed topological space ▫$X$▫, we endow ▫$X^{<\alpha} = \cup\{X^\beta \colon \beta < \alpha\}$▫ with the strongest topology that coincides with the product ... topology on every subset ▫$X^\beta$▫ of ▫$X^{<\alpha}, \beta < \alpha$▫. It turns out that many important model spaces of infinite-dimensional topology (including the topology of non-metrizable manifolds) can be obtained as spaces of the form ▫$X^{<\alpha}$for $X=I, \mathbb{R}$▫. This paper deals with some topological properties of spaces ▫$X^{<\alpha}$▫. Some new classification and characterization theorems are proved for these spaces.
    Source: Proceedings of the Infinite Dimensional Analysis and Topology (IDAT) Conference 2009 (Str. 186-196)
    Type of material - conference contribution
    Publish date - 2009
    Language - english
    COBISS.SI-ID - 15526233

    Link(s):

    http://dx.doi.org/10.1016/j.top.2009.11.018

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