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

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