In mathematics, and more particularly in set theory, a cover (or covering) of a set $${\displaystyle X}$$ is a family of subsets See more

A refinement of a cover $${\displaystyle C}$$ of a topological space $${\displaystyle X}$$ is a new cover $${\displaystyle D}$$ of $${\displaystyle X}$$ such that every set in $${\displaystyle D}$$ is … See more

• Atlas (topology) – Set of charts that describes a manifold
• Bornology – Mathematical generalization of boundedness See more

Covers are commonly used in the context of topology. If the set $${\displaystyle X}$$ is a topological space, then a cover $${\displaystyle C}$$ See more

The language of covers is often used to define several topological properties related to compactness. A topological space X is said to be
Compact if every … See more

A topological space X is said to be of covering dimension n if every open cover of X has a point-finite open refinement such that no point of … See more

• "Covering (of a set)", Encyclopedia of Mathematics, EMS Press, 2001 [1994] See more