Density of Morse functions on sets definable in o-minimal structures
Volume 89 / 2006
Annales Polonici Mathematici 89 (2006), 289-299
MSC: 32B20, 14P10, 14B05.
DOI: 10.4064/ap89-3-5
Abstract
We present a tameness property of sets definable in o-minimal structures by showing that Morse functions on a definable closed set form a dense and open subset in the space of definable $C^p$ functions endowed with the Whitney topology.
