The Friedmann–Lemaître–Robertson–Walker metric is a solution of the field equations of GR. It tells us the local behavior of spacetime, that is, g(x) at a given spacetime point x If the matter density is high enough, the curvature is positive. It is said then that the universe is closed. How is this global property of the manifold inferred from the local metric? Why is an infinite universe of positive local curvature ruled out?