What is Weak order unit?

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.}