Let be integral curves in a manifold then is closed.

**Proof:**

Let be have a limit in . Let be a chart then converges to by continuity. But also converges to . Hence and so . Thus is closed.

Let be integral curves in a manifold then is closed.

**Proof:**

Let be have a limit in . Let be a chart then converges to by continuity. But also converges to . Hence and so . Thus is closed.