covering

A covering map (also called a covering or projection) is a surjective open map f:X->Y that is locally a homeomorphism, meaning that each point in X has a neighborhood that is the same after mapping f in Y. In a covering map, the preimages f^(-1)(y) are a discrete set of X, and the cardinal number of f^(-1)(y) (which is possibly infinite) is independent of the choice of y element Y.

cover | covering space | simply connected | topological space | universal cover