What are the differences between derived and closure points in sets?

[Unassuming]

Homework Statement

I am looking for examples of sets that have derived pts that are different from closure pts because I am trying to understand them better.

Also, if you can , please try to bring the word "base" into this. I do not understand quite fully a base. I know the definition and I know it is similar to a generator. (I hope)

Homework Equations

The Attempt at a Solution

I know that {1/n : n in Naturals} has D-pt {0} and closure pts {all set}

 

[Dick]

I'm not sure you are using very standard terminology. Can you state the definitions of your words? I would say the closure of S={1/n} is S union {0}.

 

[Unassuming]

Your right, I'm sorry. My closure was wrong