covering

That which covers or conceals; a cover; something spread or laid over or wrapped about another.

Action of the verb to cover.

A collection of sets U_i such that their union contains U; such a collection with the additional property that every U_i is open; such a collection with the additional property that every U_i is contained in U.

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 D_x and an open neighborhood U of x such that π⁻¹(U)= displaystyle ⨆_(d∈D_x)V_d and π|_(V_d):V_d→U is a homeomorphism for every d∈D_x. See Covering space on Wikipedia.Wikipedia

present participle and gerund of cover