We study the extraordinary dimension function dimL introduced by Šˇcepin. An axiomatic
characterization of this dimension function is obtained.We also introduce inductive dimensions indL
and IndL and prove that for separable metrizable spaces all three coincide. Several results such as
characterization of dimL 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.