Cover/Covering (𝐶)
- a cover of a set/space 𝑋 is a family of subsets of 𝑋 whose union is all of 𝑋
- a cover of a subset 𝑌 of 𝑋 is a family of subsets of 𝑋 whose union contains all of 𝑌
Open Cover/Covering
- an open cover is a cover whose elements are all open sets
Subcover/Subcovering
- let 𝐶 be a cover of a space 𝑋; a subcover of 𝐶 is a subset of 𝐶 that still covers 𝑋