Verify if the following sets are closed, open and find and the set of accumulation points. (Does the last set have a name?)
a)
b) If
c)
I have the definitions but I'm not sure how to proceed.
I believe that the set of limit points of can be called the derived set of , and is sometimes denoted by .
The boundary of the first set is . Note that none of the boundary points are in the set. What does this tell you about the set being open or closed?