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In mathematics, specifically in order theory and functional analysis, an ordered vector space is said to be regularly ordered and its order is called regular if is Archimedean ordered and the order dual of distinguishes points in .[1] Being a regularly ordered vector space is an important property in the theory of topological vector lattices.


Every ordered locally convex space is regularly ordered.[2] The canonical orderings of subspaces, products, and direct sums of regularly ordered vector spaces are again regularly ordered.[2]


If is a regularly ordered vector lattice then the order topology on is the finest topology on making into a locally convex topological vector lattice.[3]

See also


  1. ^ Schaefer & Wolff 1999, pp. 204–214.
  2. ^ a b Schaefer & Wolff 1999, pp. 222–225.
  3. ^ Schaefer & Wolff 1999, pp. 234–242.