Relative uniform convergence and Archimedean property in pre-ordered vector spaces

It is proved that, for a pre-ordered vector space $X$, the quotient space $(X\mathrm{/}A,[W])$ is an Archimedeanization of $X$, where $W$ is the closure of the positive wedge $X_{+}$ in ru-topology, $A=W\cap (-W)$, and $[W]$ is the quotient set of $W$ in $X\mathrm{/}A$.