i'm having a problem with the definition of open, closed and clopen sets.
I have understood the basic definitions, but then the teacher today in class said that the normed space is limitless. A colleague of mine said then that the normed space is clopen, but i can't really see why. To me, a normed space, since it has no limits, it is impossible to find a ball that has points not belonging to the normed space, so it can't be a closed set, right? Then, it must be an open set. Or am I mixing everything up? Thanks in advance!