Question

Every normed space is a metric space.Is converse ture?

Answer 1

So, as a result, you can say, every normed space is a metric space. Every normed space is a metric space, clear. Because, whenever we take norm, it can be converted intometric. But converse need not be true; but converse need not be true, in general; that is,all the metric spaces may not be a normed space.