Let \(X\) be a topological space. A covering space of \(X\) is a topological space \(\tilde X\) together with a continuous map \(p\colon \tilde X\to X\) such that every \(x\in X\) has an open neighborhood \(U\) for which \(\inverseof{p}(U)\) is a union of pairwise disjoint open sets \(V_i\subseteq\tilde X\), each mapped homeomorphically onto \(U\) by \(p\). The sets \(V_i\) are the sheets of \(\tilde X\) over \(U\).
Let \(p_1\colon\tilde X_1\to X\) and \(p_2\colon\tilde X_2\to X\) be covering spaces of \(X\). An isomorphism of covering spaces is a homeomorphism \(f\colon\tilde X_1\to\tilde X_2\) with \(p_2\circ f = p_1\):
[@Hat02].