We consider the problem of determining which conditions are necessaryfor cobordisms to admit Lorentzian metrics with certain properties. Inparticular, we prove a result originally due to Tipler without a smoothnesshypothesis necessary in the original proof. In doing this, we prove thatcompact horizons in a smooth spacetime satisfying the null energy condition aresmooth. We also prove that the ”generic condition” is indeed generic in the setof Lorentzian metrics on a given manifold