I have a smooth function $F: \mathbb{R}^n \rightarrow \mathbb{R}$. The paper I am reading says "... for $F$ supported on $X \subseteq \mathbb{R}^n$" where $X$ is some set that is an intersection of a closed set and an open set.
What does $F$ is supported on $X$ mean in this case? Does it just mean that $F$ is non-zero on $X$ or the support of $F$ is the closure of $X$ or the support of $F$ contains the closure of $X$? or something else even?
I wasn't too sure... any clarification would be appreciated. Thank you.