In the definition of covering map is one to take the "disjoint union" of open sets $\displaystyle \left\{O_j\right\}_{j\in\mathcal{J}}$ to literally be $\displaystyle \coprod_{j\in\mathcal{J}}O_j=\bigcup_{j\in\mathcal {J}}O_j\times\{j\}$ or is one to assume that the class of open sets is merely pairwise disjoint?