Covering Space

A topological space C together with a continuous surjective map p: C → X (the covering map) onto a base space X such that every point of X has an open neighborhood U for which p^{-1}(U) is a disjoint union of open sets in C, each of which is mapped homeomorphically onto U by p. The fibers p^{-1}(x) are discrete sets and p is a local homeomorphism.