Given a vector space $${\displaystyle X}$$ over a subfield $${\displaystyle F}$$ of the complex numbers $${\displaystyle \mathbb {C} ,}$$ a … See more

Every (real or complex) vector space admits a norm: If $${\displaystyle x_{\bullet }=\left(x_{i}\right)_{i\in I}}$$ is a Hamel basis for … See more

For any norm $${\displaystyle p:X\to \mathbb {R} }$$ on a vector space $${\displaystyle X,}$$ the reverse triangle inequality holds: $${\displaystyle p(x\pm y)\geq |p(x)-p(y)|{\text{ for all }}x,y\in X.}$$ If $${\displaystyle u:X\to Y}$$ is a continuous linear … See more

All seminorms on a vector space $${\displaystyle X}$$ can be classified in terms of absolutely convex absorbing subsets $${\displaystyle A}$$ of $${\displaystyle X.}$$ To each such subset corresponds a seminorm $${\displaystyle p_{A}}$$ called … See more

• Asymmetric norm – Generalization of the concept of a norm
• F-seminorm – A topological vector space whose topology can be defined by a metric
• Gowers norm
• Kadec norm – All infinite … See more

• Bourbaki, Nicolas (1987) [1981]. Topological Vector Spaces: Chapters 1–5. Éléments de mathématique. Translated by Eggleston, H.G.; Madan, S. Berlin New York: Springer-Verlag. ISBN 3-540-13627-4. OCLC 17499190.
• Khaleelulla, S. M. (1982). … See more