I've recently came accross an analysis text that includes in one of the examples the following:
S is the set of all complex numbers (that is, R2)
T is the set of all real integers (Z)
the sets are:
CLOSED OPEN PERFECT BOUNDEDS YES YES YES NO
T YES NO NO NO
Question: How is it that 1) S and T are closed, how can they be closed but not bounded? 2) S is closed and open at the same time?
Any help is much appreciated...