weak order unit

{{one source|date=July 2020}}

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 $x \geq 0$ and also for all $y \in X,$ $\inf \{ x, |y| \} = 0 \text{ implies } y = 0.$ {{sfn|Schaefer|Wolff|1999|pp=234–242}}

Examples

If $X$ is a separable Fréchet topological vector lattice then the set of weak order units is dense in the positive cone of $X.$ {{sfn|Schaefer|Wolff|1999|pp=204–214}}

See also

{{annotated link|Quasi-interior point}}
{{annotated link|Vector lattice}}

Citations

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References

{{Narici Beckenstein Topological Vector Spaces|edition=2}}
{{Schaefer Wolff Topological Vector Spaces|edition=2}}

{{Ordered topological vector spaces}}

{{Functional analysis}}

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Category:Functional analysis