A covering space of a space is a pair where

  • is a space
  • is a map such that
    for all there is a nbd of such that ,
    where open, and is a Homeomorphism
    is called a covering map.
    Open sets as above are called evenly covered.

Lift
Uniqueness of Lifts Lemma
Homotopy Lifting Lemma

Universal Cover
Sheeted cover

Covering Fundamental groups