Proposition: Boundary, Accumulation, Interior, and Isolated Points

• Let S R. Then each point of S is either an interior point or a boundary point.

• Let S R. Then bd(S) = bd(R \ S).

• A closed set contains all of its boundary points. An open set contains none of its boundary points.

• Every non-isolated boundary point of a set S R is an accumulation point of S.

• An accumulation point is never an isolated point.

Proof: