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A pair of points (x,y) in a Riemannian manifold (M,g) is said to have thefinite blocking property if there is a finite set P contained in M\{x,y} suchthat every geodesic segment from x to y passes through a point of P. We showthat for every closed C-infinity manifold M of dimension at least two and everypair (x,y) in M x M, there exists a dense G-delta set of C-infinity Riemannianmetrics on M such that (x,y) fails to have the finite blocking property forevery g in that set.

A dense G-delta set of Riemannian metrics without the finite blocking property