Akhil Mathew writes
In particular, we can think of subspaces of an analytic space as being cut out by coherent sheaves of ideals.
And in this (p.1) note, I also encountered the same terminology.
An analytic subspace of $\mathbf C^n$ is a ringed space $(X, \mathscr{H}_X)$ such that $X\subset \mathbf C^n$ is given the Euclidean topology and is locally cut out by holomorphic functions.
What does cut out mean in these contexts? How do you formally put it?