Quasinorm

In linear algebra, functional analysis and related areas of mathematics, a quasinorm is similar to a norm in that it satisfies the norm axioms, except that the triangle inequality is replaced by
for some .
Related concepts.
If is a quasinorm on then induces a vector topology on whose neighborhood basis at the origin is given by the sets:
as ranges over the positive integers. 
A topological vector space (TVS) with such a topology is called a quasinormed space. 
Every quasinormed TVS is a pseudometrizable. 
A vector space with an associated quasinorm is called a quasinormed vector space.
A complete quasinormed space is called a quasi-Banach space.
A quasinormed space formula_2 is called a quasinormed algebra if the vector space "A" is an algebra and there is a constant "K" > 0 such that 
for all formula_4.
A complete quasinormed algebra is called a quasi-Banach algebra.
Characterizations.
A topological vector space (TVS) is a quasinormed space if and only if it has a bounded neighborhood of the origin.