Hello everyone...

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...