What is interior region?

The interior region of a set in a topological space \( X\) is the largest subset contained in the set in which every point has a neighbourhood within the set. We define \( \text{Int} A \) as an interior point as a point in a set\(X \) such that every neighbourhood of the point is contained in \( A\).

$$ \text{Int} A = \{ x \in X : (\exists r>0) (B_r(x) \subseteq A ) \} $$