2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220050The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.13 pagesCombinatoricsGeneral Mathematics06A06, 06A07, 06A10 and 52A01text