Geodesic
Finite-to-One Open Mappings
Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 77-83

Voir la notice de l'article provenant de la source Cambridge University Press

The class of finite-to-one open mappings on manifolds contains some important subclasses. Any non-constant analytic function from a bounded region in its domain of definition is finite-to-one. Church [2] showed that any light strongly open Cn map f: Rn → Rn is discrete. A number of papers concerning discrete open mappings on manifolds have been published; see [1-6; 8-9; 11-14].A result of Černavskiĭ [1] (see also [13]) shows that for any discrete strongly open mapping f : Mn → Nn of an n-manifold into an n-manifold, the branch set of f has dimension less than n – 1. If f is also a closed map, then N(f) is finite and the set of points x for which N(x, f) = N(f) is an open dense connected subset of Mn. 
Duda, Edwin; Haynsworth, W. Hugh. Finite-to-One Open Mappings. Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 77-83. doi: 10.4153/CJM-1971-008-6
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