Does the real projective space $\mathbb{R}P^n, n \geq 1$ have a boundary?

Question

I know of the fact that real $n$-dimensional projective space $\mathbb{R}P^n$ is a compact smooth manifold, but I don't know whether it has a boundary or not. It is clear to me however that in the cases $n=1, 2$ the real projective line and the real projective plane have no boundary. Then is it true that the real projective space has no boundary for any $n \geq 1$? If so, what are some good references that prove this?