Adjective
(algebra, mathematical analysis) Of a mathematical structure, endowed with a norm.
(statistics) Of a data set that has been adjusted to a norm.
Source: en.wiktionary.orgAgain from the Heine–Borel theorem, the closed unit ball of any finite-dimensional normed vector space is compact. Source: Internet
Being the dual of a normed space, the bidual X ′′ is complete, therefore, every reflexive normed space is a Banach space. Source: Internet
A surjective isometry between the normed vector spaces V and W is called an isometric isomorphism, and V and W are called isometrically isomorphic. Source: Internet
If a normed space X is separable, then the weak-* topology is metrizable on the norm-bounded subsets of X*. Source: Internet
Basic notions Every normed space X can be isometrically embedded in a Banach space. Source: Internet
Examples Every normed vector space has a natural topological structure : the norm induces a metric and the metric induces a topology. Source: Internet