A note on Bierstone–Milman–Pawłucki's paper “Composite differentiable functions”
Tom 102 / 2011
Annales Polonici Mathematici 102 (2011), 293-299 MSC: Primary 32B20; Secondary 26E10, 14P15. DOI: 10.4064/ap102-3-8
We demonstrate that the composite function theorems of Bierstone–Milman–Pawłucki and of Glaeser carry over to any polynomially bounded, o-minimal structure which admits smooth cell decomposition. Moreover, the assumptions of the o-minimal versions can be considerably relaxed compared with the classical analytic ones.