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.

A stratification of a topological space is a finite filtration by closed subsets F_i , such that the difference between successive members F_i and F_{(i − 1)} of the filtration is either empty or a smooth submanifold of dimension i. The connected components of the difference F_i − F_{(i − 1)} are the strata of dimension i. A stratification is called a Whitney stratification if all pairs of strata satisfy the Whitney conditions A and B, as defined below.