Finitary approximations of coarse structures - Protasov, I. V. (Matematychni Studii, 2021)
A coarse structure E on a set X is called finitary if, for each entourage EE, there exists a natural number n such that E[x]< n for each xX. By a finitary approximation of a coarse structure E^′, we mean any finitary coarse structure E such that EE^′. If E^′ has a countable base and E[x] is finite for each xX then E^′ has a cellular finitary approximation E such that the relations of linkness on subsets of ( X,E^′) and ( X, E) coincide. This answers Question 6 from [8]: the class of cellular coarse spaces is not stable under linkness. We define and apply the strongest finitary approximation of a coarse structure.