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  • Preservation and reflection of size properties of balleans
    Dikranjan, Dikran N., 1950- ; Zava, Nicolò
    We study the combinatorial size of subsets of a ballean, as defined in [I. Protasov, T. Banakh, Ball Structures and Colorings of Groups and Graphs, Math. Stud. Monogr. Ser., vol.11, VNTL, Lviv, 2003] ... ; [I. Protasov, M. Zarichnyi, General Asymptology, VNTL Publishers, Lviv, Ukraine, 2007] (largeness, smallness, extralargeness, etc.), paying particular attention to the preservation of these properties under taking images and inverse images along various classes of maps (bornologous, effectively proper, (weakly) soft, coarse embeddings, canonical projections of products, canonical inclusions of co-products, etc.). We show by appropriate examples that many of the properties describing the size are not preserved under coarse equivalences (even injective or surjective ones), whereas largeness and smallness are preserved under arbitrary coarse equivalences.
    Vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 221, 2017, str. 570-595)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2017
    Jezik - angleški
    COBISS.SI-ID - 17974105

    Povezava(-e):

    http://dx.doi.org/10.1016/j.topol.2017.02.008

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