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A theorem on generic intersections in an o-minimal structure

Volume 227 / 2014

Krzysztof Jan Nowak Fundamenta Mathematicae 227 (2014), 21-25 MSC: Primary 03C64; Secondary 14P15, 22E15. DOI: 10.4064/fm227-1-2


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 $\sigma \in G$.


  • Krzysztof Jan NowakInstitute of Mathematics
    Faculty of Mathematics and Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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