Metric space vs normed vector space vs inner product space
ID: metric-space-vs-normed-vector-space-vs-inner-product-space
Metric space vs normed vector space vs inner product space by 
Ciro Santilli 37 Updated 2025-05-29 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-29 +Created 1970-01-01TODO examples:
- metric space that is not a normed vector space
- norm 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.
Hierarchy of topological, metric, normed and inner product spaces
. Source. 
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