I am reading optimization by vector space methods written by Luenberger.
And there is the following sentence:
A normed space is always closed but not necessarily complete.
I am wondering why a normed space is always closed.
I know if you see in topological perspective, the entire set is always closed/open but in this book, the closed set is defined as a complement to open set and open set is defined when the interior of the set is actually itself.
I am asking why a normed space is closed in the above definition of closed and open set.