Whitney conditions

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In topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney.

[edit] The Whitney conditions in Rⁿ

Let X and Y be two locally closed submanifolds of R ⁿ , of dimensions i and j.

• X and Y satisfy Whitney's condition A if whenever a sequence of points x₁, x₂, ... in X converges to a point y in Y, the sequence of tangent i-planes T₁, T₂, ... to X at the points x_m converges to an i-plane containing the tangent j-plane to Y at y.

• X and Y satisfy Whitney's condition B if for each sequence x₁, x₂, ... of points in X and each sequence y₁, y₂, ... of points in Y, each converging to the same point y in Y, the sequence of secant lines L_m between x_m and y_m converges to a line contained in the tangent j-plane to Y at y.

[edit] See also

• Whitney stratified space
• Thom-Mather stratified space
• Topologically stratified space

[edit] References

• Whitney, Hassler Local properties of analytic varieties. 1965 Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse) pp. 205--244 Princeton Univ. Press, Princeton, N. J.