A theorem on generic intersections in an o-minimal structure
Volume 227 / 2014
Fundamenta Mathematicae 227 (2014), 21-25
MSC: Primary 03C64; Secondary 14P15, 22E15.
DOI: 10.4064/fm227-1-2
Abstract
Consider a transitive definable action of a Lie group $G$ on a definable manifold $M$. Given two (locally) definable subsets $A$ and $B$ of $M$, we prove that the dimension of the intersection $\sigma (A) \cap B$ is not greater than the expected one for a generic $\sigma \in G$.
