Mark each statement True or False. Justify each answer.
(a) Some unbounded sets are compact.
(b) If S is a compact subset of ℝ, then there is at least one point in ℝ that is an accumulation point of S.
(c) If S is compact and x is an accumulation point of S, then x ϵ S.
(d) If S is unbounded, then S has at least one accumulation point.
(e) Let ℱ = {Ai: i ∈ ℕ} and suppose that the intersection of any finite subfamily of ℱ is nonempty. If ∩ ℱ = ∅, then for some k ∈ ℕ, Ak is not compact.
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