I am reading something on Sobolev spaces.
We define $D(\Omega)$ to be the set of function in $C^{\infty}(\Omega)$ that has compact support in $\Omega$.
I know that compact support is completion of the set where a function is non-zero.
but, what does it mean by "have compact support in $\Omega$"? Does it mean it is a function such that its compact support is a subset of $\Omega$?