Sphere covering by minimal number of caps and short closed sets
Geometric Topology
2015-12-22 v1
Abstract
A subset of the sphere is said short if it is contained in an open hemisphere. A short closed set which is geodesically convex is called a cap. The following theorem holds: 1. The minimal number of short closed sets covering the -sphere is . 2. If short closed sets cover the -sphere then (i) their intersection is empty; (ii) the intersection of any proper subfamily of them is non-empty. In the case of caps (i) and (ii) are also sufficient for the family to be a covering of the sphere.
Cite
@article{arxiv.1512.06361,
title = {Sphere covering by minimal number of caps and short closed sets},
author = {A. B. Németh},
journal= {arXiv preprint arXiv:1512.06361},
year = {2015}
}