On proper branched coverings and a question of Vuorinen.

We study global injectivity of proper branched coverings from the open Euclidean -ball onto an open subset of the Euclidean -space in the case where the branch set is compact. In particular, we show that such mappings are homeomorphisms when or when the branch set is empty. This gives a positive answer to the corresponding cases of a question of Vuorinen.