Ordered vector space information

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...

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...

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...

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...

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

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

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...

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...

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...

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

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...

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...

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...

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

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...

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...

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...

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

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

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...

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...

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...

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...

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

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...