Topology and its Applications 138

We study the extraordinary dimension function dimL introduced by Šˇcepin. An axiomaticcharacterization of this dimension function is obtained.We also introduce inductive dimensions indLand IndL and prove that for separable metrizable spaces all three coincide. Several results such ascharacterization of dimL in terms of partitions and in terms of mappings into n-dimensional cubes arepresented. We also prove the converse of the Dranishnikov-Uspenskij theorem on dimension-raisingmaps.