Example 6.11.
Let \(X\) be a topological space. Then the poset \(\Open(X)\) of open subsets admits a Grothendieck topology, called the open covering topology, for which the covering sieves of some \(U \in \Open(X)\) are those sieves generated by open coverings \(U = \bigcup_{i \in I} U_i\). We denote the resulting topos by
\[\Shv(X) \quad := \quad \Shv_{\open}(\Open(X)).\]