An open neighborhood of a point x : X : 𝑥 𝑋 x:X of a Topological Space X 𝑋 X is an open set U ∈ 𝒪 ( X ) 𝑈 𝒪 𝑋 U\in\mathcal{O}({X}) with x ∈ U 𝑥 𝑈 x\in U .