Geodesic
Local Topological Properties of Maps and Open Extensions of Maps
Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1121-1128

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

A σ-discrete set in a topological space is a set which is a countable union of discrete closed subsets. A mapping ƒ : X ⟶ Y from a topological space X into a topological space Y is said to be σ-discrete (countable) if each fibre ƒ-1(y), y ε Y is σ-discrete (countable). In 1936, Alexandroff showed that every open map of a bounded multiplicity between Hausdorff spaces is a local homeomorphism on a dense open subset of the domain [2]. 
Kohli, J. K. Local Topological Properties of Maps and Open Extensions of Maps. Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1121-1128. doi: 10.4153/CJM-1977-110-1
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