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 ≥ 0 and for all y in X, inf { x, |y| } = 0 implies y = 0.

Examples

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

See also

• Quasi-interior point
• Vector lattice

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. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.