Non-Euclidean Intersection Lemmas (Q2717770)

The so-called Intersection Lemma refers to common interior points of diameter segments of point sets in the Euclidean plane \(E^2\). The author extends this to point sets on the unit sphere \(S^2\subset E^3\) and in the hyperbolic plane, respectively. In the first case, the analogous statement requires that the diameter of the given point set is smaller than \({\pi\over 2}\); otherwise the intersection point can be an endpoint of a diameter segment. Also the author gives a related conjecture for Riemannian surfaces.NEWLINENEWLINEFor the entire collection see [Zbl 0944.00034].