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 $$x \geq 0$$ 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 $$X.$$