Asymptotic dimension and small subsets in locally compact topological groups

Taras Banakh, Ostap Chervak, Nadya Lyaskovska

We prove that for a coarse space $X$ the ideal $S(X)$ of small subsets of $X$ coincides with the ideal $D_{<}(X)$ of subsets $A\subset X$ of asymptotic dimension $asdim(A)<asdim(X)$…