I need help with this question cause I don't know where to start off:
Prove that if a set contains each of its accumulation points, then it must be a closed set.
All of that is very true. But that is not the question.
The question is: Prove that the derived set of a set is closed. And that is not true.
Think of the space of real numbers, with a topology generated by the collection .
The derived set of is the set which is not closed because is limit point of that set.