20.500.12556/RUL-111081 Classifying homogeneous ultrametric spaces up to coarse equivalence 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 ▫${\rm cov}^\sharp(X)={\rm cov}^\flat(X)$▫. ultrametric space isometrically homogeneous metric space coarse equivalence true false true Angleški jezik Ni določen Članek v reviji 2019-09-23 09:30:13 2019-09-23 09:30:14 2022-08-23 03:40:40 0000-00-00 00:00:00 2016 0 0 Str. 189-202 no. 2 Vol. 144 2016 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.124 0010-1354 10.4064/cm6697-9-2015 17652057 25242624 RAZ_Banakh_Taras_i2016.pdf RAZ_Banakh_Taras_i2016.pdf 1 281F1A18FC5DBE9EF49E373C29BBE263 62896d38b28b7459050afe4c8a75c09b5738a61fc750dea0aba9feb62bba09db 4c7c3fe7-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=122874 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0