Let S and T be subsets of ℝ. Find a counterexample for each of the following.
(a) If P is the set of all isolated points of S, then P is a closed set.
(b) Every open set contains at least two points.
(c) If S is closed, then cl (int S) = S.
(d) If S is open, then int (cl S) = S.
(e) bd (cl S) = bd S
(f) bd (bd S) = bd S
(g) bd (S ∪ T) = (bd S) ∪ (bd T)
(h) bd (S ∩ T) = (bd S) ∩ (bd T)
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