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  • Classifying homogeneous ultrametric spaces up to coarse equivalence
    Banakh, Taras, 1968- ; Repovš, Dušan, 1954-
    For every metric space ▫$X$▫ we introduce two cardinal characteristics ▫${\rm cov}^\flat(X)$▫ and ▫${\rm cov}^\sharp(X)$▫ describing the capacity of balls in ▫$X$▫. We prove that these cardinal ... characteristics are invariant under coarse equivalence and prove that two ultrametric spaces ▫$X,Y$▫ are coarsely equivalent if ▫${\rm cov}^\flat(X)={\rm cov}^\sharp(X)={\rm cov}^\flat(Y)={\rm cov}^\sharp(Y)$▫. This result implies that an ultrametric space ▫$X$▫ is coarsely equivalent to an isometrically homogeneous ultrametric space if and only if ▫${\rm cov}^\flat(X)={\rm cov}^\sharp(X)$▫. Moreover, two isometrically homogeneous ultrametric spaces ▫$X,Y$▫ are coarsely equivalent if and only if ▫${\rm cov}^\sharp(X)={\rm cov}^\sharp(Y)$▫ if and only if each of these spaces coarsely embeds into the other space. This means that the coarse structure of an isometrically homogeneous ultrametric space ▫$X$▫ is completely determined by the value of the cardinal ▫${\rm cov}^\sharp(X)={\rm cov}^\flat(X)$▫.
    Vir: Colloquium mathematicum. - ISSN 0010-1354 (Vol. 144, no. 2, 2016, str. 189-202)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 17652057

    Povezava(-e):

    http://dx.doi.org/10.4064/cm6697-9-2015
    Repozitorij Univerze v Ljubljani – RUL
    DOI

vir: Colloquium mathematicum. - ISSN 0010-1354 (Vol. 144, no. 2, 2016, str. 189-202)
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