Counting coarse subsets of a countable group

Igor V. Protasov, Ksenia Protasova


For every countable group G, there are 2ω distinct classes of coarselyequivalent subsets of G.


ballean; coarse structure; asymorphism; coarse equivalence

Subject classification

54E15; 20F69

Full Text:



T. Banakh, J. Higes and M. Zarichnyi, The coarse classification of countable abelian groups, Trans. Amer. Math. Soc. 362 (2010), 4755-4780.

D. Dikranjan and N. Zava, Some categorical aspects of coarse spaces and ballean, Topology Appl. 225 (2017) 164-194.

P. de la Harpe, Topics in geometric group theory, University Chicago Press, 2000.

I. V. Protasov, Morphisms of ball structures of groups and graphs, Ukr. Mat. Zh. 53 (2002), 847-855.

I. Protasov and T. Banakh, Ball structures and colorings of groups and graphs, Math. Stud. Monogr. Ser., Vol. 11, VNTL, Lviv, 2003.

I. Protasov and M. Zarichnyi, General asymptology, Math. Stud. Monogr. Ser., Vol. 12, VNTL, Lviv, 2007.

J. Roe, Lectures on coarse geometry, Amer. Math. Soc., Providence, R.I, 2003.

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