= Metric space vs normed vector space vs inner product space
TODO examples:
* <metric space> that is not a <normed vector space>
* <norm (mathematics)> vs <metric>: a norm gives size of one element. A <metric> is the distance between two elements. Given a norm in a space with subtraction, we can obtain a distance function: the <metric induced by a norm>.
\Image[https://upload.wikimedia.org/wikipedia/commons/7/74/Mathematical_Spaces.png]
{title=Hierarchy of topological, metric, normed and inner product spaces}