Boundary points

Properties

Conceptual Venn diagram showing the relationships among different points of a subset ${\displaystyle S}$ of ${\displaystyle \mathbb {R} ^{n}.}$${\displaystyle A}$ = set of accumulation points of ${\displaystyle S}$ (also called limit points), ${\displaystyle B=}$ set of boundary points of ${\displaystyle S,}$ area shaded green = set of interior points of ${\displaystyle S,}$ area shaded yellow = set of isolated points of ${\displaystyle S,}$ areas shaded black = empty sets. Every point of ${\displaystyle S}$ is either an interior point or a boundary point. Also, every point of ${\displaystyle S}$ is either an accumulation point or an isolated point. Likewise, every boundary point of ${\displaystyle S}$ is either an accumulation point or an isolated point. Isolated points are always boundary points.