Closure properties

Geometry Level 3

Here are three statements about the closure S\overline S of a set SS inside a metric space X.X.

I. Let S,TS,T be subsets of X.X. Then ST=ST.\overline{S \cap T} = {\overline S} \cap {\overline T}.
II. Let S,TS,T be subsets of X.X. Then ST=ST. \overline{S \cup T} = {\overline S} \cup {\overline T}.
III. If S=X, {\overline S} = X, then S=X.S=X.

Which of these statements is/are true?

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