Question: For a set S R, let CP(S) be the set of cluster points of S. Prove or disprove. (a) For any set S, CP(S) S.

For a set S R, let CP(S) be the set of cluster points of S. Prove or disprove.

(a) For any set S, CP(S) S.

(b) If S is finite, then CP(S) = .

(c) If S is infinite, then CP(S) 6= .

(d) For any interval S = [a, b], CP(S) = S.

(e) For any set S, CP(CP(S)) CP(S).

(f) There is a set S so that CP(CP(CP(S))) 6= but CP(CP(CP(CP(S)))) =

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