Abstract
AbstractWe show how to derive triangulations of sets locally definable in o-minimal structures from triangulations of compact definable sets. We give it in particular for strict $$\mathcal C^p$$
C
p
-triangulations which has been recently studied by the author. This combined with a theorem of Fernando and Ghiloni implies that every continuous mapping defined on a locally compact subset B of $$\mathbb R^m$$
R
m
with values in any locally definable and locally compact subset A of $$\mathbb R^n$$
R
n
can be approximated by $$\mathcal C^p$$
C
p
-mappings defined on B with values in A for any positive integer p.
Publisher
Springer Science and Business Media LLC
Reference14 articles.
1. Aschenbrenner, M., Fischer, A.: Definable versions of theorems by Kirszbraun and Helly. Proc. London Math. Soc. 102(3), 468–502 (2011)
2. Czapla, M., Pawłucki, W.: Strict $$\cal{C} ^1$$-triangulations in o-minimal structures. Topol. Methods Nonlinear Anal. 52, 739–747 (2018)
3. Fernando, J.F., Ghiloni, R.: Differentiable approximation of continuous semialgebraic maps. Selecta Math. (N. S.) 25(3), 30 (2019)
4. Fernando, J.F., Ghiloni, R.: Smooth approximations in PL geometry. Am. J. Math. 144(4), 967–1007 (2022)
5. Gromov, M.: Entropy, homology and semialgebraic geometry. Astérisque 145–146(5), 225–240 (1987)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献