Geodesic
Whitney's extension theorem in o-minimal structures
Athipat Thamrongthanyalak1
1 Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok 10400, Thailand and Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43212, U.S.A.
Annales Polonici Mathematici, Tome 119 (2017) no. 1, pp. 49-67

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In 1934, H. Whitney gave a necessary and sufficient condition on a jet of order $m$ on a closed subset of $E$ of $\mathbb R^n$ to be the jet of order $m$ of a $C^m$-function. Later, K. Kurdyka and W. Pawłucki proposed a subanalytic version of this theorem. In this paper, we work in an o-minimal expansion of a real closed field and prove a definable version of Whitney’s Extension Theorem.
DOI : 10.4064/ap3940-2-2017
Keywords: whitney gave necessary sufficient condition jet order closed subset mathbb jet order m function later nbsp kurdyka paw ucki proposed subanalytic version theorem paper work o minimal expansion real closed field prove definable version whitney extension theorem

Athipat Thamrongthanyalak 1

1 Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok 10400, Thailand and Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43212, U.S.A. 
@article{10_4064_ap3940_2_2017,
     author = {Athipat Thamrongthanyalak},
     title = {Whitney's extension theorem in o-minimal structures},
     journal = {Annales Polonici Mathematici},
     pages = {49--67},
     publisher = {mathdoc},
     volume = {119},
     number = {1},
     year = {2017},
     doi = {10.4064/ap3940-2-2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap3940-2-2017/}
}
TY  - JOUR
AU  - Athipat Thamrongthanyalak
TI  - Whitney's extension theorem in o-minimal structures
JO  - Annales Polonici Mathematici
PY  - 2017
SP  - 49
EP  - 67
VL  - 119
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap3940-2-2017/
DO  - 10.4064/ap3940-2-2017
LA  - en
ID  - 10_4064_ap3940_2_2017
ER  - 
%0 Journal Article
%A Athipat Thamrongthanyalak
%T Whitney's extension theorem in o-minimal structures
%J Annales Polonici Mathematici
%D 2017
%P 49-67
%V 119
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap3940-2-2017/
%R 10.4064/ap3940-2-2017
%G en
%F 10_4064_ap3940_2_2017
Athipat Thamrongthanyalak. Whitney's extension theorem in o-minimal structures. Annales Polonici Mathematici, Tome 119 (2017) no. 1, pp. 49-67. doi: 10.4064/ap3940-2-2017

Cité par Sources :