Let X and Y be topological spaces and let f : X → Y be a function. Prove that the following statements are equivalent: (a) f: XY is continuous. (b) For any E CY, f-¹(Int(E)) ≤ Int(f-¹(E)). (c) For any ECY, ƒ˜¹(E) ≤ f¯¹(E).

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