CONVEXITY AND TWO PIECE PROPERTY IN S^n
M. Beltgy, Sameh Shenawy, Ayman Elsharkawy · International Journal of Pure and Apllied Mathematics · 2014
A subset A of S n , n ≥ 2, has spherical two piece property if any hypersphere cuts A into at most two pieces.A subset A of S n has totally geodesic two piece property if any totally geodesic hypersurface in S n , n ≥ 2, cuts A into at most two pieces.In this article we study some geometric properties of subsets in S n -as a manifold with focal points and these types of two piece property in S n .