Classifying homogeneous ultrametric spaces up to coarse equivalence

• Autorzy: Taras Banakh , Dušan Repovš
• Języki publikacji: EN

Abstrakty

EN

For every metric space X we introduce two cardinal characteristics $cov^{♭}(X)$ and $cov^{♯}(X)$ describing the capacity of balls in X. We prove that these cardinal characteristics are invariant under coarse equivalence, and that two ultrametric spaces X,Y are coarsely equivalent if $cov^{♭}(X) = cov^{♯}(X) = cov^{♭}(Y) = cov^{♯}(Y)$. This implies that an ultrametric space X is coarsely equivalent to an isometrically homogeneous ultrametric space if and only if $cov^{♭}(X) = cov^{♯}(X)$. Moreover, two isometrically homogeneous ultrametric spaces X,Y are coarsely equivalent if and only if $cov^{♯}(X) = cov^{♯}(Y)$ if and only if each of them coarsely embeds into the other. This means that the coarse structure of an isometrically homogeneous ultrametric space X is completely determined by the value of the cardinal $cov^{♯}(X) = cov^{♭}(X)$.

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 51F99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 2
• Strony: 189-202

Daty

wydano

2016

Twórcy

autor

Taras Banakh

• Ivan Franko National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine
• Jan Kochanowski University in Kielce, Świętokrzyska 15, 25-406 Kielce, Poland

autor

Dušan Repovš

• Faculty of Education
• Faculty of Mathematics and Physics, University of Ljubljana, Kardeljeva pl. 16, 1000 Ljubljana, Slovenia

Identyfikatory

DOI

10.4064/cm6697-9-2015