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Here are three statements about the closure S‾\overline SS of a set SSS inside a metric space X.X.X.
I. Let S,TS,TS,T be subsets of X.X.X. Then S∩T‾=S‾∩T‾.\overline{S \cap T} = {\overline S} \cap {\overline T}.S∩T=S∩T. II. Let S,TS,TS,T be subsets of X.X.X. Then S∪T‾=S‾∪T‾. \overline{S \cup T} = {\overline S} \cup {\overline T}.S∪T=S∪T. III. If S‾=X, {\overline S} = X,S=X, then S=X.S=X.S=X.
Which of these statements is/are true?
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