Intersection of Generic Rotations in Some Classical Spaces

Consider an o-minimal structure on the real field R and two definable subsets A, B of the Euclidean space Rn, of the unit sphere Sn or of the hyperbolic space Hn, n ≥ 2, which are of dimensions k, l ≤ n−1, respectively. We prove that the dimension of the intersection σ(A) ∩ B is less than min{k, l} for a generic rotation σ of the ambient space; here we set dim ∅ = −1.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.