$\mathcal{U} : U = \bigcup _{i \in I} U_ i$ 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 $I$),
$\mathcal{U} : U = \bigcup _{i \in I} U_ i$ 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 $I$),
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