Interior, Exterior, and Boundary Points

Let be a metric space, let be a subset of , and let be a point in .

• is an interior point of E if s.t. (The notation is a ball).
• that is an exterior point of E if s.t. .
• is a boundary point of E if it is neither an interior point nor an exterior point.

The set of all interior points of is called the interior of and is denoted as . The set of all exterior points of is called the exterior of and is denoted as . The set of all boundary points of is called the boundary of and is denoted as .