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Hurewicz's dimension-raising theorem states that for every n-to-1 map f : X\to Y, dim Y =< dim X + n holds. In this paper we introduce a new notion offinite-to-one like map in a large scale setting. Using this notion we formulatea dimension-raising type theorem for the asymptotic dimension and theasymptotic Assouad-Nagata dimension. It is also well-known as Hurewicz'sfinite-to-one mapping theorem that dim X =< n if and only if there exists an (n+ 1)-to-1 map from a 0-dimensional space onto X. We formulate a finite-to-onemapping type theorem for the asymptotic dimension and the asymptoticAssouad-Nagata dimension.

Dimension-Raising Maps in a Large Scale