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v • d • e Normed and Banach spaces

Overview of the basic and important concepts of normed vector spaces, which if complete are called Banach spaces

Primitives	Norm, Vector space, Field, Completeness

Spaces	Normed space, Banach space (if the metric induced by the norm is complete)

Supertypes	Metric space, Complete metric space, Topological space

Subtypes	Inner product space (all IPSes induce a norm), Hilbert space (if the metric induced by inner product is complete)

Easy examples	Euclidean norm

Examples	Analysis: Functional Analysis: Measure Theory:

[ilmath]\Vert\cdot\Vert_\infty[/ilmath] examples	(see: Category:Supremum norms) Supremum norm on [ilmath]\mathbb{R}^n[/ilmath] or [ilmath]\mathbb{C}^n[/ilmath]

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