Note on Archimedean property in ordered vector spaces

Eduard Emelyanov

It is shown that an ordered vector space $X$ is Archimedean if and only if $\underset{\tau \in \{\tau \},y\in L}{\inf }(x_{\tau }-y)=0$ for any bounded decreasing net $x_{\tau }\downarrow$ in $X$, whe…