Introduction to Singularity Theory with Historical Remarks
Naively speaking this map is stable since if we push (or perturb) the graph of the map slightly (as shown by dotted line), the topological pictures of the dotted graph and the solid graph are the same. More rigorously, the dotted curve is just the graph of a reparametrization of f.
KeywordsSingular Point Tangent Bundle Smooth Manifold Implicit Function Theorem Topological Type
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