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 $y\in X,$ $\inf \{x,|y|\}=0\text{ implies }y=0.$

Examples

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

See also

• Quasi-interior point

References

• Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834. 
• Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.