Classifying homogeneous ultrametric spaces up to coarse equivalenceBanakh, Taras (Avtor) Repovš, Dušan (Avtor) ultrametric spaceisometrically homogeneous metric spacecoarse equivalenceFor 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 ▫${\rm cov}^\sharp(X)={\rm cov}^\flat(X)$▫.20162019-09-23 09:30:13Članek v reviji111081sl