## 5.1. Open and Closed Sets

### Proposition 5.1.7: 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.