A function f : X → Y : 𝑓 → 𝑋 𝑌 f:X\to Y between Topological Spaces is continuous if for all open sets U ∈ 𝒪 ( Y ) 𝑈 𝒪 𝑌 U\in\mathcal{O}({Y}) , the Preimage f − 1 ( U ) ∈ 𝒪 ( X ) superscript 𝑓 1 𝑈 𝒪 𝑋 f^{-1}(U)\in\mathcal{O}({X}) is also open.