Weak order unit

In mathematics, specifically in order theory and functional analysis, an element $x$ of a vector lattice $X$ is called a weak order unit in $X$ if $x\ge 0$ and also for all $y\in X,$ $\inf \{x,|y|\}=0\text{ implies }y=0.$Template:Sfn

Examples

• If $X$ is a separable Fréchet topological vector lattice then the set of weak order units is dense in the positive cone of $X.$Template:Sfn

See also

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References

• Template:Narici Beckenstein Topological Vector Spaces
• Template:Schaefer Wolff Topological Vector Spaces