Differentiable functions defined in closed sets. A problem of Whitney
| dc.creator | Bierstone, E. | |
| dc.creator | Milman, P. D. | |
| dc.creator | Pawlucki, W. | |
| dc.date | 2001-11-20 | |
| dc.date.accessioned | 2026-07-07T04:44:41Z | |
| dc.date.available | 2026-07-07T04:44:41Z | |
| dc.description | In 1934, Whitney raised the question of how to recognize whether a function f defined on a closed subset X of Euclidean space is the restriction of a function that is continuously differentiable to order p. A necessary and sufficient criterion was given in the case n=1 by Whitney, using limits of finite differences, and in the case p=1 by Glaeser (1958), using limits of secants. We introduce a necessary geometric criterion, for general n and p, involving limits of finite differences, that we conjecture is sufficient at least if X has a "tame topology". We prove that, if X is a compact subanalytic set, then there exists q=q(p) such that the criterion of order q implies that f is p times continuously differentiable. The result gives a new approach to higher-order tangent bundles (or bundles of differentiable operators) on singular spaces. | |
| dc.description | AMS-TEX, 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0111213 | |
| dc.identifier | http://arxiv.org/abs/math/0111213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62688 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 58C25, 32B20 | |
| dc.title | Differentiable functions defined in closed sets. A problem of Whitney | |
| dc.type | text |