The topic of this article may not meet Wikipedia's notability guideline for numbers. Please help to demonstrate the notability of the topic by citing reliable secondary sources that are independent of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be merged, redirected, or deleted.Find sources: "Regularly ordered" – news · newspapers · books · scholar · JSTOR (July 2020) (Learn how and when to remove this template message)

This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources.Find sources: "Regularly ordered" – news · newspapers · books · scholar · JSTOR (June 2020)

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]}