Past exam of the topology and groups course of the University of Oxford / 2023 / 3 / a / i / Solution

A covering map is a continuous surjection $p:\tilde{X}\to X$ such that every $x\in X$ has an open neighbourhood $U$ for whichwhere the $U_{\alpha }$ are pairwise disjoint open subsets of $\tilde{X}$. Such a $U$ is an evenly covered neighbourhood, and the sets $U_{\alpha }$ are its covering sheets. The index set may be infinite. The requirement that every sheet map onto all of $U$ is part of the definition.