**Definition of interior points:**

Let (X,τ) be a topological space and A⊆X Then, a point x∈A (x is an element of set A) is said to be an interior point of A if there exists an open set ‘U’ containing ‘x’ such that

X∈U⊆A

**Example1:**

Consider the set X={1,2,3,4} and the topology τ={φ,{1},{1,2,3},{4},{1,4},X}

let A= {1,3,4} ⊆ X. what are the interior points of set A?

**solution:**

To find the interior points of set A, we check all the elements of set A one by one.

**For 1:**(there exists 4 open sets ‘U’ containing ‘1’)

1∈{1}⊆{1,3,4} 1∈{1,4}⊆{1,3,4}

1∈{1,2,3}⊈{1,3,4} 1∈X ⊈{1,3,4}

1 is an interior point of set A.

**For 3:**

3∈{1,2,3}⊈{1,3,4} 3∈X ⊈{1,3,4}

3 is not an interior point of set A.

**For 4:**

4∈{4}⊆{1,3,4} 4∈{1,4}⊆{1,3,4}

4∈X ⊈{1,3,4}

4 is an interior point of set A.

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