General expression to show a point is on a surface

Question

First: Sorry for the strange question formulation.

Let $S$ be a surface bounding a domain $D$. Now I'm searching for an expression to say point $P$ lays on $S$. I used the expression $P\in S$ but this just looks awful, because $S$ is not a set...

Any ideas?

Answer 1

Well, $S$ is a set. In fact, $S = \{p \mid p\ \text{is on the boundary of $D$}\}$. Hence, it is fine to say $P \in S$.