Example 1

Let B be a topological space and $(U_i)_{i\in I}$ a family of subsets of B. Let E denote the sum space of the family $(U_i)_{i\in I}$ and $p: E\rightarrow B$ the mapping deduced from the canonical injections of the $U_i$ into B. In order that the mapping $p$ be etale, it is necessary and sufficient that the $U_i,i\in I$, all be open.