A closed (n + 1)-convex set inR 2 is a union ofn 6 convex sets

It is shown that if a closed setS in the plane is (n+1)-convex, then it has no more thann ⁴ holes. As a consequence, it can be covered by≤n ⁶ convex subsets. This is an improvement on the known bound of 2 ⁿ ·n ³. The author would like to thank the BSF for partially supporting this research. Publication no. 354.