Prove that there is a unique topology given interior operator – math.stackexchange.com

Prove that there is a unique topology given interior operator – math.stackexchange.com

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Suppose $f: \mathcal{P}(X) \to \mathcal{P}(X)$ satisfies, for every set $A,B \subseteq X$ $(I_1): f(X) = X$ $(I_2): f(A) \subseteq A$ $(I_3): f(A \cap B) =f(A) \cap f(B)$ ...

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