Let \(X\) be a topological space and let \(U\subseteq X\) be an open set. We call the family of open sets \(U_{i}\), \(i\in I\) an open cover of \(U\) if
\[U=\bigcup _{i\in I}U_{i},\]
i.e. if \(U\) equals the union of all \(U_{i}\).
Definitions: 1 2 3
Proofs: 4 5 6 7 8 9 10 11