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- W2264044900 abstract "For every ballean $X$ we introduce two cardinal characteristics $cov^flat(X)$ and $cov^sharp(X)$ 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 $cof(X)=cof(Y)$ and $cov^flat(X)=cov^sharp(X)=cov^flat(Y)=cov^sharp(Y)$. This result implies that a cellular ordinal ballean $X$ is homogeneous if and only if $cov^flat(X)=cov^sharp(X)$. Moreover, two homogeneous cellular ordinal balleans $X,Y$ are coarsely equivalent if and only if $cof(X)=cof(Y)$ and $cov^sharp(X)=cov^sharp(Y)$ 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 $cof(X)$ and $cov^sharp(X)$. 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 $cf(gamma)$ 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 $2^omega$." @default.
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- W2264044900 date "2017-01-01" @default.
- W2264044900 modified "2023-10-18" @default.
- W2264044900 title "Classifying homogeneous cellular ordinal balleans up to coarse equivalence" @default.
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- W2264044900 doi "https://doi.org/10.4064/cm6785-4-2017" @default.
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