In mathematics, specifically in

order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article intr ...

and

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined ...

, an element

x

of a

vector lattice In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper ''Su ...

X

is called a weak order unit in

X

x \geq 0

and also for all

y \in X,

\inf \ = 0 \text y = 0.

Examples

* If

X

is a separable Fréchet

topological vector lattice In mathematics, specifically in functional analysis and order theory, a topological vector lattice is a Hausdorff topological vector space (TVS) X that has a partial order \,\leq\, making it into vector lattice that is possesses a neighborho ...

then the set of weak order units is dense in the positive cone of

X.

Citations

References

* * {{mathematics-stub Functional analysis

Examples

See also

Citations

References