20.500.12556/RUL-109506 Classifying homogeneous cellular ordinal balleans up to coarse equivalence For every ballean ▫$X$▫ we introduce two cardinal characteristics ▫$\text{cov}^\flat(X)$▫ and ▫$\text{cov}^\sharp(X)$▫ describing the capacity of balls in ▫$X$▫. We observe that these cardinal characteristics are invariant under coarse equivalence and prove that two cellular ordinal balleans ▫$X,Y$▫ are coarsely equivalent if ▫$\text{cof}(X)=\text{cof}(Y)$▫ and ▫$\text{cov}^\flat(X) = \text{cov}^\sharp(X) = \text{cov}^\flat(Y) = \text{cov}^\sharp(Y)$▫. This result implies that a cellular ordinal ballean ▫$X$▫ is homogeneous if and only if ▫$\text{cov}^\flat(X)=\text{cov}^\sharp(X)$▫. Moreover, two homogeneous cellular ordinal balleans ▫$X,Y$▫ are coarsely equivalent if and only if ▫$\text{cof}(X)=\text{cof}(Y)$▫ and ▫$\text{cov}^\sharp(X) = \text{cov}^\sharp(Y)$▫ if and only if each of these balleans coarsely embeds into the other ballean. This means that the coarse structure of a homogeneous cellular ordinal ballean ▫$X$▫ is fully determined by the values of the cardinals ▫$\text{cof}(X)▫$ and ▫$\text{cov}^\sharp(X)$▫. For every limit ordinal ▫$\gamma$▫ we shall define a ballean ▫$2^{<\gamma}$▫ (called the Cantor macro-cube), which in the class of cellular ordinal balleans of cofinality ▫$\text{cf}(\gamma)$▫ plays a role analogous to the role of the Cantor cube ▫$2^{\kappa}$▫ in the class of zero-dimensional compact Hausdorff spaces. We shall also present a characterization of balleans which are coarsely equivalent to ▫$2^{<\gamma}$▫. This characterization can be considered as an asymptotic analogue of Brouwer's characterization of the Cantor cube ▫$2^\omega$▫. coarse space ballean cellular ballean ordinal ballean homogeneous ballean coarse equivalence cellular entourage asymptotic dimension Cantor macro-cube true false true Angleški jezik Ni določen Članek v reviji 2019-09-04 12:34:07 2019-09-04 12:34:09 2022-08-21 03:42:36 0000-00-00 00:00:00 2017 0 0 Str. 211-224 no. 2 Vol. 149 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.124 0010-1354 10.4064/cm6785-4-2017 18045529 25242624 RAZ_Banakh_Taras_i2017.pdf RAZ_Banakh_Taras_i2017.pdf 1 0EF45558D7BB8F1EFE3A364A2D83B2A0 ccc1315b352d93499107377bedf56f974228e6c13ba3fb7ecc8a929127114a82 e2846a0c-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121085 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0