Non-compact manifold with compact boundary

Question

What is an example of a non-compact manifold with compact boundary?

Answer 1

It seems that $[0;\infty)$ is the required example.

Answer 2

A non-compact manifold without boundary would work, as the empty set is compact.

Answer 3

Another example: take your favorite non-compact manifold without boundary, and remove an open ball from it. Then the boundary of the result is a sphere.