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  "body": "\n## Summary\n\nA Whitney stratification of a singular space is a partition into smooth manifolds, the strata, see the [[definition|F19BQTN832]].\nThe strata fit together in a controlled way along their boundaries.\nThe control is given by Whitney's conditions (a) and (b) on limits of tangent planes and secant lines.\nHassler Whitney proved that every complex [[analytic set|3RWWZYPAFV]] has such a stratification, and the result was later extended to semialgebraic and subanalytic sets.\nBy the Thom–Mather isotopy theorem, a Whitney stratified space is topologically locally trivial along each stratum.\nThis makes these stratifications the standard setting for [[perverse sheaves|5WHXRZDZFK]] and intersection homology.\n\n## Explanations\n\n### L1 human\n\nA singular space, such as a cone or a surface with a crease, can be cut into smooth pieces of different dimensions: the smooth part, the crease, the tip.\nWhitney's conditions ask that the large pieces approach the small ones nicely, without spiralling or twisting in a way that changes the local picture.\nThen the space looks the same near every point of a given piece.\nFor the cone $x^2 + y^2 = z^2$, the pieces are the two halves of the cone without its tip, and the tip.\n",
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