Whitney conditions

In differential topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney in 1965. He was motivated by the following example: given a singular manifold ${\displaystyle X}$, the singular set ${\displaystyle \operatorname {Sing} (X)}$ is either a manifold or a singular space. In the latter condition, one can take the singular subset again, ${\displaystyle \operatorname {Sing} (\operatorname {Sing} (X))}$, and repeat this step a finite number of times until a smooth manifold is found. The collection of spaces form a Whitney stratification.

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