The kernel of a starshaped subset of the plane
Benjamin R. Halpern · Proceedings of the American Mathematical Society · 1969
A point p of a subset V of Euclidean two-dimensional space RI is a star-center for V provided the line segment [p, q] -{ tp + (1-t)qI 0 R2, a 0 such that 'y(to-8, to+ ) {'y(to) } is completely contained in one of the two open half-planes determined by the tangent line of 'y at y(to). The author wishes to thank F. Valentine and A. Heppes for their suggestions on how to shorten the original proof of Theorem 1.