Let be the topological space and, then a point is said to be an interior point of set A, if there exist an open set such that
                                                             
            In other words let A be a subset of a topological space X, a point is said to be an interior points of A if is in some open set contained in A.

Interior of a Set:
            Let be a topological space and A be a subset of X, then the interior of A is denoted by  or  is defined to be the union of all open sets contained in A.
            In other words let be a topological space and A be a subset of X. The interior of A is union of all open subsets of A, and a point in the interior of A is called an interior point of A.

Remarks:

• Interior of A is union of all open sets contained in A. Union of open sets is again an open set. Hence interior of A is the largest open set contained in A.
•  and
• Interior of sets is always open.
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Example:
            Let  with topology . If, then find.
            Since there is no open set containing and a subset of A, so is not an interior point of A. Similarly, is not an interior point of A. Since is n open set containing and is a subset of A, so is an interior point of A. Hence

Theorems:

• Each point of a non empty subset of a discrete topological space is its interior point.
• The interior of a subset of a discrete topological space is the set itself.
• The interior of a subset A of a topological space X is the union of all open subset of A.
• The subset A of topological space X is open if and only if.
• If A is a subset of a topological space X, then.
• Let be a topological space and A and B are subsets of X, then (1)  (2)  (3)