Let the unit interval have postive orientation induced from the standard orientation of $\mathbb{R}$, and let $\{0\}$ and $\{1\}$ be equipped with orientation $+$. Why is $\{0\}$ then an in-boundary and $\{1\}$ an out-boundary? I don't understand how one defines a positive normal at the boundary of a 1-manifold like $[0,1]$? I do know that the tangent space of a one-point manifold is the trivial vector space $\{0\}$ with unique basis being the empty set, but I'm not able to put that to use here.
Thanks a lot in advance! All help appreciated.