- #1
xanadu
- 3
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I've been reading Shilov's book and the definition of a limit point is as follows: x is a limit point of A if every neighborhood of x (any open ball centered at x with arbitrary radius r) contains at least one point y distinct from x which belongs to A.
I feel that from this definition a point at the center of the set would be a limit point. If that is the case then from what I understand the set B of all limit points of A is a superset of A.
However there is an exercise which says find a set A that is not empty and the set of limit points of A is empty. What could I be missing here?
I feel that from this definition a point at the center of the set would be a limit point. If that is the case then from what I understand the set B of all limit points of A is a superset of A.
However there is an exercise which says find a set A that is not empty and the set of limit points of A is empty. What could I be missing here?