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Now suppose p: C → X is a covering map and C ( and therefore also X ) is connected and locally path connected.
The action of Aut ( p ) on each fiber is free.
If this action is transitive on some fiber, then it is transitive on all fibers, and we call the cover regular ( or normal or Galois ).
Every such regular cover is a principal G-bundle, where G = Aut ( p ) is considered as a discrete topological group.

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