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In mathematics, specifically in order theory and functional analysis, an ordered vector space X {\displaystyle X} is said to be regularly ordered and its order is called regular if X {\displaystyle X} is Archimedean ordered and the order dual of X {\displaystyle X} distinguishes points in X {\displaystyle X}. Being a regularly ordered vector space is an important property in the theory of topological vector lattices.
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