Closure properties

Geometry Level 4

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

I. Let $$S,T$$ be subsets of $$X.$$ Then $$\overline{S \cap T} = {\overline S} \cap {\overline T}.$$

II. Let $$S,T$$ be subsets of $$X.$$ Then $$\overline{S \cup T} = {\overline S} \cup {\overline T}.$$

III. If $${\overline S} = X,$$ then $$S=X.$$

Which of these statements is true?

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