Theorem (Axioms of a Closure): Let (M,d) be a metric space and let S,T C M. Then (1) 0 = 0 and M = M. (2) If S ST, then ŠSŤ. (3) Š is the smallest closed set in M such that S CS. (4) S is closed in Me S = S. (5) 5 = 5. (6) SUT = SUT. (7) In general, (S n T) S §nT. But, (SOT) # $ nT. (8) S = Fe. %3D

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