Abstract. In this paper we define and study exposed points of subsets in a smooth Riemannian manifold without focal points. Sectional curvature at exposed points is studied. Proofs of well-known theorems are given as corollaries of the established results.

AMS Subject Classification (1991): 53C42

Keyword(s): Manifolds without focal points, convex subsets, geodesics, sectional curvature

Received June 10, 1993 and in revised form November 24, 1993. (Registered under 5588/2009.)