• $\mathcal{U} : U = \bigcup _{i \in I} U_ i$ is an open covering of $U$ (note: we allow any $U_ i$ to be empty and we even allow, in case $U$ is empty, the empty set for $I$),

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).