Geodesic
Maps with Locally Flat Singular Sets
Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 916-921

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

A map f : M → N is topologically equivalent tog: X → Y if there exist homeomorphisms α: M → X and β: N → Y such that βfα –1 = g. At x ∊ M, f is locally topologically equivalent to g if, for every neighbourhood W ⊂ M of x, there exist neighbourhoods U ⊂ W of x and V of f(x) such that f|U: U → V is topologically equivalent to g.1.1. Definition. Given a map f: M → N and x ∊ M, let F be the component of f –1(f(x)) containing x. The singular set Af is defined as follows: x ∊ M – Af if and only if there are neighbourhoods U of F and V of f(x) such that f| U: U → F is topologically equivalent to the product projection map of V × F onto V. 
Timourian, J. G. Maps with Locally Flat Singular Sets. Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 916-921. doi: 10.4153/CJM-1970-105-7
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