In mathematics, specifically in order theory and functional analysis, an element x {\displaystyle x} of a vector lattice X {\displaystyle X} is called a weak order unit in X {\displaystyle X} if x ≥ 0 {\displaystyle x\geq 0} and also for all y ∈ X , {\displaystyle y\in X,} inf { x , | y | } = 0 implies y = 0. {\displaystyle \inf\{x,|y|\}=0{\text{ implies }}y=0.}
Examples If X {\displaystyle X} is a separable Fréchet topological vector lattice then the set of weak order units is dense in the positive cone of X . {\displaystyle X.}
See also Quasi-interior point Vector lattice – Partially ordered vector space, ordered as a latticePages displaying short descriptions of redirect targets
Citations
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.