Let X, Y be complex affine varieties and f:X → Y a regular mapping. We prove that if dim X ≥ 2 and f is closed in the Zariski topology then f is proper in the classical topology.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-13, author = {T. Krasi\'nski and S. Spodzieja}, title = {A characterization of proper regular mappings}, journal = {Annales Polonici Mathematici}, volume = {77}, year = {2001}, pages = {127-138}, zbl = {1033.14037}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-13} }
T. Krasiński; S. Spodzieja. A characterization of proper regular mappings. Annales Polonici Mathematici, Tome 77 (2001) pp. 127-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-13/