About: Ordered vector space

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In mathematics, an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations.

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rdf:type	yago:WikicatOrderedGroups yago:Abstraction100002137 yago:Group100031264 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 yago:WikicatPropertiesOfTopologicalSpaces
rdfs:label	Geordneter Vektorraum (de) Espace vectoriel ordonné (fr) Ordered vector space (en) 有序向量空间 (zh)
rdfs:comment	Ein geordneter Vektorraum ist eine mathematische Struktur. Es handelt sich um einen -Vektorraum, auf dem zusätzlich eine mit der Vektorraum-Struktur verträgliche Ordnungsrelation gegeben ist, die man üblicherweise mit bezeichnet (man liest kleiner-gleich). Dadurch ist es möglich, die Elemente eines Vektorraums der Größe nach zu vergleichen. Viele in der Mathematik untersuchte Vektorräume tragen eine natürliche Ordnungsstruktur. (de) In mathematics, an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations. (en) En mathématiques, un espace vectoriel ordonné (ou espace vectoriel partiellement ordonné) est un espace vectoriel sur muni d'une relation d'ordre compatible avec sa structure. Il est dit totalement ordonné si l'ordre associé est un ordre total. (fr) 在数学中，有序向量空间（ordered vector space）是带有偏序的向量空间，并且偏序与向量空间的运算是相容的。又称偏序向量空间（partially ordered vector space）。 (zh)
foaf:depiction
dcterms:subject	Vector spaces Ordered groups Functional analysis
Wikipage page ID	8099221 (xsd:integer)
Wikipage revision ID	1119696756 (xsd:integer)
Link from a Wikipage to another Wikipage	Preorder Product order Bounded function Vector spaces Archimedean ordered vector space Ordered groups Riesz space Vector space Limit of a sequence Order isomorphism Cone-saturated Mathematics Function (mathematics) Convex cone Equivalence class Order unit Order bound dual Order complete Order dual (functional analysis) Lexicographic order Empty set Polar set Majorization Measurable function Automorphism Balanced set Topological vector space Total order Dual cone and polar cone Duality (order theory) Lattice (order) Linear function Equivalence relation Euclidean space Partially ordered set Dimension (vector space) Direct product Direct sum Directed set Isomorphism Linear functional Quotient space (linear algebra) Intersection (set theory) Archimedean order Archimedean ordered Absorbing set Functional analysis Supremum Discrete topology Translation (geometry) Regularly ordered Polar coordinate system Continuous function (topology) Integer Neighborhood (mathematics) Open set Real number Set (mathematics) Infimum Union (set theory) Solid set Partial order Normal cone (functional analysis) Lexicographical order Topological space Subset Topological vector lattice Proper cone Vector lattice Ordered group Almost-everywhere Quotient topology Positive homothety Algebraic dual Bourbaki, Nicolas Sequences Sublinear functional
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