Why are c and d closed?

Question

I don’t think there is any limit point in case of either c or d.

That's right, there are no limit points. Hence the set contains all its limit points, so it's closed. — David C. Ullrich, Mar 03 '20 at 13:21

score 2 · Accepted Answer · answered Mar 03 '20 at 13:23

A set is closed if it contains all its limit points.

Rephrased : a set is closed if it contains "the set of all it's limit points".

Therefore, if "all limit points" is empty, then the set is closed automatically, because any set contains the empty set. That's why $c,d$ are closed.

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