Editing Covering space (section)

== Smooth coverings ==
Let {{math|''E''}} and {{math|''M''}} be [[smooth manifolds]] with or without [[Boundary of a manifold|boundary]]. A covering <math>\pi : E \to M</math> is called a '''smooth covering''' if it is a [[smooth map]] and the sheets are mapped ''diffeomorphically'' onto the corresponding open subset of {{math|''M''}}. (This is in contrast to the definition of a covering, which merely requires that the sheets are mapped ''homeomorphically'' onto the corresponding open subset.)