Interior point and interior

Let \(X\) be a topological space and \(A\subseteq X\). A point \(p\in A\) is an interior point of \(A\) if there exists a neighborhood \(U\) of \(p\) with \(U\subseteq A\). The interior \(A^\circ\) of \(A\) is the set of interior points of \(A\).