Question: a) A point a in a metric space X is said to be isolated if and only if there is an r > 0 so

a) A point a in a metric space X is said to be isolated if and only if there is an r > 0 so small that Br(a) = {a}. Show that a point a ∈ X is not a cluster point of X if and only if a is isolated.
b) Prove that the discrete space has no cluster points.

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