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In mathematics, specifically inorder theory andfunctional analysis, an element${\displaystyle x}$ of avector lattice${\displaystyle X}$ is called aweak order unit in${\displaystyle X}$ if${\displaystyle x\ge 0}$ and also for all${\displaystyle y\in X,}$${\displaystyle inf\{x,|y|\}=0\text{ implies }y=0.}$^[1]

• If${\displaystyle X}$ is aseparableFréchettopological vector lattice then the set of weak order units is dense in the positive cone of${\displaystyle X.}$^[2]

• Quasi-interior point
• Vector lattice – Partially ordered vector space, ordered as a latticePages displaying short descriptions of redirect targets

• 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.

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