Abstract
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 .
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