Let $M$ be a manifold noncompact. Then there is a closed embebdding of the half line $[0, \infty)$ into $M$.

Question

Let $M$ be a manifold connected hausdorf noncompact. Then there is a closed embebdding of the half line $[0, \infty)$ into $M$.

I'm hard to build such a function without self-intersections.

Book: Differential Topology, Hirsch. p 27.