# Math Help - Covering Map Question

1. ## Covering Map Question

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

2. It's the latter. The point is that each x has a neighborhood U whose inverse image consists of homeomorphic "copies" of U in the covering space.

3. Originally Posted by Tinyboss
It's the latter. The point is that each x has a neighborhood U whose inverse image consists of homeomorphic "copies" of U in the covering space.
Yeah, homeomorphic copies who are disjoint. That makes much more sense, because then you'd have to define a whole new topology on this disjoint union, etc. Thanks!