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Ordered vector space information


A point in and the set of all such that (in red). The order here is if and only if and

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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Ordered vector space

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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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Ordered topological vector space

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analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order...

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Vector space

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In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied...

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Riesz space

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Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are...

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Archimedean ordered vector space

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} An Archimedean (pre)ordered vector space is a (pre)ordered vector space whose order is Archimedean. A preordered vector space X {\displaystyle X} is...

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Ordered field

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space – Vector space with a partial order Partially ordered ring – Ring with a compatible partial order Partially ordered space – Partially ordered topological...

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Partially ordered set

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than two sets. Applied to ordered vector spaces over the same field, the result is in each case also an ordered vector space. See also orders on the Cartesian...

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Total order

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two sets. Applied to the vector space Rn, each of these make it an ordered vector space. See also examples of partially ordered sets. A real function of...

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Normed vector space

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In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization...

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Partially ordered space

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{\displaystyle x\leq y} . Ordered vector space – Vector space with a partial order Ordered topological vector space Topological vector lattice Gierz, G.; Hofmann...

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Order complete

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theory and functional analysis, a subset A {\displaystyle A} of an ordered vector space is said to be order complete in X {\displaystyle X} if for every...

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Topological vector space

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A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar...

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Coordinate vector

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coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis...

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Vector notation

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be Euclidean vectors, or more generally, members of a vector space. For representing a vector, the common typographic convention is lower case, upright...

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Order topology

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normal Hausdorff space. The standard topologies on R, Q, Z, and N are the order topologies. If Y is a subset of X, X a totally ordered set, then Y inherits...

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Topological vector lattice

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continuous. If X {\displaystyle X} is a vector lattice and an ordered topological vector space that is a Fréchet space in which the positive cone is a normal...

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Product order

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on the Cartesian product of totally ordered sets Ordinal sum of partial orders Ordered vector space – Vector space with a partial order Neggers, J.; Kim...

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Ordered ring

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Partially ordered space – Partially ordered topological space Riesz space – Partially ordered vector space, ordered as a lattice, also called vector lattice...

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Banach lattice

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abstract (L)-spaces. Banach space – Normed vector space that is complete Normed vector lattice Riesz space – Partially ordered vector space, ordered as a lattice...

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Order theory

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A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear. By checking these properties...

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Partially ordered group

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order An ordered vector space is a partially ordered group A Riesz space is a lattice-ordered group A typical example of a partially ordered group is...

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Distributive lattice

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is a Boolean algebra if and only if n is square-free. A lattice-ordered vector space is a distributive lattice. Young's lattice given by the inclusion...

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Monotonic function

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subspace of X . {\displaystyle X.} In functional analysis on a topological vector space X {\displaystyle X} , a (possibly non-linear) operator T : X → X ∗ {\displaystyle...

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Hasse diagram

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represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set ( S , ≤ ) {\displaystyle...

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Convex cone

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article, only the case of scalars in an ordered field is considered. A subset C of a vector space V over an ordered field F is a cone (or sometimes called...

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