Suppose that X^~, X are arcwise-connected and locally arcwise-connected topological spaces. Then (X^~, p) is said to be a covering space of X if p:X^~->X is a surjective continuous map with every x element X having an open neighborhood U such that every connected component of p^(-1)(U) is mapped homeomorphically onto U by p.

covering map | deck transformation | fundamental group | universal cover