Intersection of Generic Rotations in Some Classical Spaces
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 64 (2016) no. 2-3, pp. 105-107
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Consider an o-minimal structure on the real field $\mathbb {R}$ and two definable subsets $A$, $B$ of the Euclidean space $\mathbb {R}^{n}$, of the unit sphere $\mathbb {S}^{n}$ or of the hyperbolic space $\mathbb {H}^{n}$, $n \geq 2$, which are of dimensions $k,l \leq n-1$, respectively. We prove that the dimension of the intersection $\sigma (A) \cap B$ is less than $\min\{k,l\}$ for a generic rotation $\sigma $ of the ambient space; here we set $\dim\emptyset = -1$.
Keywords:
consider o minimal structure real field mathbb definable subsets euclidean space mathbb unit sphere mathbb hyperbolic space mathbb geq which dimensions leq n respectively prove dimension intersection sigma cap min generic rotation sigma ambient space here set dim emptyset
Affiliations des auteurs :
Krzysztof Nowak 1 ; Grzegorz Tomkowicz 2
@article{10_4064_ba8084_10_2016,
author = {Krzysztof Nowak and Grzegorz Tomkowicz},
title = {Intersection of {Generic} {Rotations} in {Some} {Classical} {Spaces}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {105--107},
publisher = {mathdoc},
volume = {64},
number = {2-3},
year = {2016},
doi = {10.4064/ba8084-10-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba8084-10-2016/}
}
TY - JOUR AU - Krzysztof Nowak AU - Grzegorz Tomkowicz TI - Intersection of Generic Rotations in Some Classical Spaces JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2016 SP - 105 EP - 107 VL - 64 IS - 2-3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/ba8084-10-2016/ DO - 10.4064/ba8084-10-2016 LA - en ID - 10_4064_ba8084_10_2016 ER -
%0 Journal Article %A Krzysztof Nowak %A Grzegorz Tomkowicz %T Intersection of Generic Rotations in Some Classical Spaces %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2016 %P 105-107 %V 64 %N 2-3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ba8084-10-2016/ %R 10.4064/ba8084-10-2016 %G en %F 10_4064_ba8084_10_2016
Krzysztof Nowak; Grzegorz Tomkowicz. Intersection of Generic Rotations in Some Classical Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 64 (2016) no. 2-3, pp. 105-107. doi: 10.4064/ba8084-10-2016
Cité par Sources :