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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: "Weak order unit" – news · newspapers · books · scholar · JSTOR (July 2020) |
In mathematics, specifically in order theory and functional analysis, an element of a vector lattice
is called a weak order unit in
if
and also for all
[1]
Examples
[edit]- If
is a separable Fréchet topological vector lattice then the set of weak order units is dense in the positive cone of
[2]
See also
[edit]- Quasi-interior point
- Vector lattice – Partially ordered vector space, ordered as a latticePages displaying short descriptions of redirect targets
Citations
[edit]- ^ Schaefer & Wolff 1999, pp. 234–242.
- ^ Schaefer & Wolff 1999, pp. 204–214.
References
[edit]- Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
- Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.
Basic concepts | |
---|---|
Types of orders/spaces | |
Types of elements/subsets | |
Topologies/Convergence | |
Operators | |
Main results |
Spaces |
| ||||
---|---|---|---|---|---|
Theorems | |||||
Operators | |||||
Algebras | |||||
Open problems | |||||
Applications | |||||
Advanced topics | |||||
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