Regularly ordered
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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.
Examples
[edit | edit source]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]
Properties
[edit | edit source]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
[edit | edit source]- Vector lattice – Partially ordered vector space, ordered as a lattice
References
[edit | edit source]- ^ Schaefer & Wolff 1999, pp. 204–214.
- ^ a b Schaefer & Wolff 1999, pp. 222–225.
- ^ Schaefer & Wolff 1999, pp. 234–242.
Bibliography
[edit | edit source]- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).