Whitney C-infinity topology

Summary

The Whitney $C^\infty$ topology, also called the strong $C^\infty$ topology, is a topology on the set $C^\infty(M, N)$ of smooth maps between smooth manifolds. Two maps are close in it when their values and derivatives up to some order are close at every point. The allowed error may shrink towards infinity. It is the standard topology in which one says that a property of maps is generic, stable or open. With it, $C^\infty(M, N)$ is a Baire space, which makes transversality arguments work.