closure (original) (raw)

Equivalently, A¯ consists of A together with all limit points of A in X or equivalently x∈A¯ if and only if every neighborhood of x intersects A. Sometimes the notation cl⁡(A) is used.

If it is not clear, which topological space is used, one writes A¯X. Note that if Y is a subspace of X, then A¯X may not be the same as A¯Y. For example, if X=ℝ, Y=(0,1) and A=(0,1), then A¯X=[0,1] while A¯Y=(0,1).