Definition: Open Cover

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

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Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück