The Stacks project

Example 59.10.3. If $X$ is a topological space, then it has an associated site $X_{Zar}$ defined as follows: the objects of $X_{Zar}$ are the open subsets of $X$, the morphisms between these are the inclusion mappings, and the coverings are the usual topological (surjective) coverings. Observe that if $U, V \subset W \subset X$ are open subsets then $U \times _ W V = U \cap V$ exists: this category has fiber products. All the verifications are trivial and everything works as expected.