normed vector space
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vector space on which a distance is defined
~19 min read
Encyclopedic overview
Hierarchy of mathematical spaces. Inner product spaces are a subset of normed vector spaces, which are a subset of metric spaces, which in turn are a subset of topological spaces.
In mathematics, a normed vector space or normed space is a vector space, typically over the real or complex numbers, on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If
Excerpted from Wikipedia’s “normed vector space” article, available under the CC BY-SA 4.0 licence.