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The normality of macrocubes and hyperballeans
Igor Protasov, Ksenia Protasova
For a bornology on a cardinal , we prove that the -macrocube is normal if and only if has a linearly ordered base. As a corollary, we get t…
Closeness and linkness in balleans
Igor Protasov, Ksenia Protasova
A set endowed with a coarse structure is called ballean or coarse space. For a ballean , we say that two subsets , of are close (linked) if there e…
A note on free vector balleans
Igor Protasov, Ksenia Protasova
A vector balleans is a vector space over endowed with a coarse structure in such a way that the vector operations are coarse mappings. We prove that, for every ballean…
Free coarse groups
Igor Protasov, Ksenia Protasova
A coarse group is a group endowed with a coarse structure so that the group multiplication and inversion are coarse mappings. Let be a coarse space and let $\mat…
Lattices of coarse structures
Igor Protasov, Ksenia Protasova
We consider the lattice of coarse structures on a set and study metrizable, locally finite and cellular coarse structures on from the lattice point of view.
Counting coarse subsets of a countable group
Igor Protasov, Ksenia Protasova
For every countable group , there are distinct classes of coarsely equivalent subsets of .