I found this picture when looking up topological spaces.
Is this picture actually supposed to be interpreted as decreasing sets? That is, all inner product spaces are normed vector spaces, all metric spaces are topological spaces etc?
But this would mean that every inner product space and normed vector space was a metric space. However, I don't recall inner product spaces and normed vector spaces having a metric, so it's not a metric space. Right?
On the other hand Inner product spaces do have norms, so it is a normed space. So it does make sense that it's a subset of Normed vector space.