noun That which covers or conceals; a cover; something spread or laid over or wrapped about another.
noun Action of the verb to cover.
noun A collection of sets {Ui} such that their union contains U; such a collection with the additional property that every Ui is open; such a collection with the additional property that every Ui is contained in U.
noun A special kind of map that establishes a relationship between two topological spaces in the sense that, under the action of the map, the one looks locally like several copies of the second: Formally, a continuous map π:E→X between topological spaces such that there exists, for every point x in X, a discrete space Dx and an open neighborhood U of x such that π−1(U)=⨆d∈DxVd and π|Vd:Vd→U is a homeomorphism for every d∈Dx. See Covering space on Wikipedia.Wikipedia