Fix a base topological space $X$.
For every open subset $U$ of $X$, define $\mathcal F(U)$ to be the set of open subsets of $U$.
The restriction map $\mathcal F(V) \to \mathcal F(U)$ sends $W$ to $W \cap U$.
This defines a sheaf.
Is there a nice description of the stalk at each point? I understand that it should depend on the particular point, but is there a nice description still?
If no, would there be a nice description assuming some separation axioms?