Interactive Real Analysis

Let S be an arbitrary set in the real line R.

1. A point b R is called boundary point of S if every non-empty neighborhood of b intersects S and the complement of S. The set of all boundary points of S is called the boundary of S, denoted by bd(S).
2. A point s S is called interior point of S if there exists a neighborhood of s completely contained in S. The set of all interior points of S is called the interior, denoted by int(S).
3. A point t S is called isolated point of S if there exists a neighborhood U of t such that U S = { t }.
4. A point r S is called accumulation point, if every neighborhood of r contains infinitely many distinct points of S.