Mark each statement True or False. Justify each answer. (a) Some unbounded sets are compact. (b) If S is a compact subset of , then there is at least one point in R that is an accumulation point of S....

Mark each statement True or False. Justify each answer.

(a) Some unbounded sets are compact.

(b) If S is a compact subset of
, 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 ∈ S.

(d) If S is unbounded, then S has at least one accumulation point.

(e) Let f = {A_i
: i ∈ N} and suppose that the intersection of any finite subfamily of f is nonempty. If ∩ f = ∅, then for some k ∈ N, A_k
is not compact