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We prove that each non-metrizable sequential rectifiable space ▫$X$▫ of countable ▫$\mathrm{cs}^\ast$▫-character contains a clopen rectifiable submetrizable ▫$k_\omega$▫-subspace ▫$H$▫ and admits a disjoint cover by open subsets homeomorphic to clopen subspaces of ▫$H$▫. This implies that each seque ...

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 c ...

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 ▫$X,Y$▫ ...