2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66159We study the extraordinary dimension function dim_{L} introduced by Ščepin. An axiomatic characterization of this dimension function is obtained. We also introduce inductive dimensions ind_{L} and Ind_{L} and prove that for separable metrizable spaces all three coincide. Several results such as characterization of dim_{L} in terms of partitions and in terms of mappings into $n$-dimensional cubes are presented. We also prove the converse of the Dranishnikov-Uspenskij theorem on dimension-raising maps.General Topology54F45, 55M10text