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Watson, R.O. and O'Farrell, Anthony G. (1992) The tangent stars of a set, and extensions of smooth functions. Journal fur die reine und angewandte Mathematik, 430. pp. 109-138. ISSN 0075-4102
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Abstract
The k–th order tangent star, Tank
(M, X), of a closed subset X of a Ck manifold M is
defined and studied. The map (M, X) 7→ Tank
(M, X) is a covariant functor from the
category of pairs to the category of stars. Given a continuous function f : X → R, and
letting G = graphf, we consider the star–morphism
π∗ : Tank
(M × R, G) → Tank
(M, X)
induced by the projection π : M × R → M.
Theorem : The function f has a Ck
extension to M if and only if π∗ is a bijection.
A method for calculating Tank
(M, X), and several examples, are presented, and
the relations to other tangent concepts are investigated.
| Item Type: | Article |
|---|---|
| Additional Information: | Cite as: Watson, R.O. and O'Farrell, A.G.. "The tangent stars of a set, and extensions of smooth functions.: " , vol. 1992, no. 430, 1992, pp. 109-138. https://doi.org/10.1515/crll.1992.430.109 |
| Keywords: | tangent; stars; set; extensions; smooth functions; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 14704 |
| Identification Number: | 10.1515/crll.1992.430.109 |
| Depositing User: | Prof. Anthony O'Farrell |
| Date Deposited: | 18 Aug 2021 14:21 |
| Journal or Publication Title: | Journal fur die reine und angewandte Mathematik |
| Publisher: | de Gruyter |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/14704 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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