# Exterior Point of a Set

Let be a topological space and be a subset of , then a point , is said to be an exterior point of , if there exist an open set , such that

In other words, let be a subset of a topological space . A point is said to be an exterior point of if there exists an open set containing such that

**Exterior of a Set:**

The set of all exterior points of is said to be the exterior of and is denoted by .

**Remark:**

It may be noted that an exterior point of is an interior point of .

Theorems:

• If is a subset of a topological space , then **(1)** **(2**) .

• If is a subset of a topological space , then .

• In a topological space , **(1**) **(2)** .

• If is a subset of a topological space , then **(1)** **(2)** .

• If is a subset of a topological space , then is the largest open subset of .