High Quality Content by WIKIPEDIA articles! In differential topology, the transversality theorem is a major result that describes the transversal intersection properties of a smooth family of smooth maps. It says that transversality is a generic property: any smooth map f:Xrightarrow Y, may be deformed by an arbitrary small amount into a map that is transversal to a given submanifold Z subseteq Y. The finite dimensional version of the transversality theorem is a very useful tool for establishing the genericity of a property which is dependent on a finite number of real parameters and which is expressible using a system of nonlinear equations. This can be extended to an infinite dimensional parametrization using the infinite dimensional version of the transversality theorem.

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