Interior Region in Topology: Definition and Notation

The interior of a set \(A\) in a topological space \(X\) is the largest open subset contained in \(A\). A point \(x\) is an interior point if there exists a neighborhood of \(x\) entirely within \(A\). Notation: \(\text{Int} A = \{ x \in X : (\exists r>0) (B_r(x) \subseteq A) \}\).