  The main problem considered in this article is the following: if
$\mathbf{F}$, $\mathbf{E}$ are normed spaces of continuous functions over
topological spaces $X$ and $Y$ respectively, and $\omega:Y\to\mathbb{C}$ and
$\Phi:Y\to X$ are such that the weighted composition operator $W_{\Phi,\omega}$
is continuous, when can we guarantee that both $\Phi$ and $\omega$ are
continuous? An analogous problem is also considered in the context of spaces of
holomorphic functions over (connected) complex manifolds. Additionally, we
consider the most basic properties of the weighted composition operators, which
only have been proven before for more concrete function spaces.
