
Journal of Convex Analysis 24 (2017), No. 1, 169183 Copyright Heldermann Verlag 2017 Archimedean Cones in Vector Spaces Eduard Yu. Emelyanov Dept. of Mathematics, Middle East Technical University, 06800 Ankara, Turkey eduard@metu.edu.tr [Abstractpdf] In the case of an ordered vector space (briefly, OVS) with an order unit, the Archimedeanization method was recently developed by V. I. Paulsen and M. Tomforde [Vector spaces with an order unit, Indiana Univ. Math. J. 58(3) (2009) 13191359]. We present a general version of the Archimedeanization which covers arbitrary OVS. Also we show that an OVS\ $(V,V_+)$ is Archimedean if and only if $$ \inf\limits_{\tau\in\{\tau\},\ y\in L}(x_\tau y)\ =0 $$ for any bounded below decreasing net $\{x_{\tau}\}_{\tau}$ in $V$, where $L$ is the collection of all lower bounds of $\{x_\tau\}_{\tau}$, and give characterization of the almost Archimedean property of $V_+$ in terms of existence of a linear extension of an additive mapping $T:U_+\to V_+$. Keywords: Ordered vector space, Preordered vector space, Archimedean, Archimedean element, almost Archimedean, Archimedeanization, Linear extension. MSC: 46A40 [ Fulltextpdf (149 KB)] for subscribers only. 