Normed space
From Maths
See: Subtypes of topological spaces for a discussion of relationships of normed spaces.
Contents
Definition
A normed space is a^{[1]}^{[2]}:
- vector space over the field [ilmath]F[/ilmath], [ilmath](X,F)[/ilmath]
- where [ilmath]F[/ilmath] is either [ilmath]\mathbb{R} [/ilmath] or [ilmath]\mathbb{C} [/ilmath]
- Equipped with a norm, [ilmath]\Vert\cdot\Vert[/ilmath]
We denote such a space by:
- [ilmath](X,\Vert\cdot\Vert,F)[/ilmath] or simply [ilmath](X,\Vert\cdot\Vert)[/ilmath] if the field is obvious from the context.
Names
A normed space may also be called:
- Normed linear space^{[1]} (or n.l.s)
References
- ↑ ^{1.0} ^{1.1} Functional Analysis - George Bachman and Lawrence Narici
- ↑ Analysis - Part 1: Elements - Krzysztof Maurin