  Let $(M,g)$ be a spacetime. That is, $M$ is a real manifold of dimension $4$
equipped with a Lorentzian metric $g$. We show that any separation of time and
space in $M$ is equivalent to introducing a (non-smooth) Riemann metric $h$. If
$h$ is smooth, it induces a smooth line bundle $T_p\rightarrow M$, whose any
fiber is generated by a time-like vector, called the time bundle. Whether
$(M,g,h)$ is time orientable or not corresponds to whether this line bundle is
trivial or not. As well-known, the last condition is characterized by the first
Stiefel-Whitney class $w^1(T_p)\in H^1(M,\mathbb{Z}/2)$. We then define a
partial time orientation of $M$ as a section of the line bundle $T\rightarrow
M$. As applications, we discuss time and space differentiations on $M$.
