Problem

Mark each statement True or False. Justify each answer.(a) Some unbounded sets are compact...

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 = {Ai: i ∈ ℕ} and suppose that the intersection of any finite subfamily of is nonempty. If ∩ = ∅, then for some k ∈ ℕ, Ak is not compact.

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Solutions For Problems in Chapter 3.14S