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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an orderedvectorspace or partially orderedvectorspace is a vectorspace equipped with a partial order that is compatible with the vectorspace operations...
analysis and order theory, an ordered topological vectorspace, also called an ordered TVS, is a topological vectorspace (TVS) X that has a partial order...
Riesz space, lattice-orderedvectorspace or vector lattice is a partially orderedvectorspace where the order structure is a lattice. Riesz spaces are...
In mathematics and physics, a vectorspace (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied...
space – Vectorspace with a partial order Partially ordered ring – Ring with a compatible partial order Partially orderedspace – Partially ordered topological...
than two sets. Applied to orderedvectorspaces over the same field, the result is in each case also an orderedvectorspace. See also orders on the Cartesian...
two sets. Applied to the vectorspace Rn, each of these make it an orderedvectorspace. See also examples of partially ordered sets. A real function of...
continuous. If X {\displaystyle X} is a vector lattice and an ordered topological vectorspace that is a Fréchet space in which the positive cone is a normal...
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...
In mathematics, a normed vectorspace or normed space is a vectorspace over the real or complex numbers on which a norm is defined. A norm is a generalization...
A topological vectorspace is a vectorspace that is also a topological space with the property that the vectorspace 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 vectorspace. For representing a vector, the common typographic convention is lower case, upright...
convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in the theory of topological vector lattices...
Partially orderedspace – Partially ordered topological space Riesz space – Partially orderedvectorspace, ordered as a lattice, also called vector lattice...
on the Cartesian product of totally ordered sets Ordinal sum of partial orders Orderedvectorspace – Vectorspace with a partial order Neggers, J.; Kim...
subspace of X . {\displaystyle X.} In functional analysis on a topological vectorspace X {\displaystyle X} , a (possibly non-linear) operator T : X → X ∗ {\displaystyle...
is a Boolean algebra if and only if n is square-free. A lattice-orderedvectorspace is a distributive lattice. Young's lattice given by the inclusion...
theory and functional analysis, a subset A {\displaystyle A} of an orderedvectorspace is said to be order complete in X {\displaystyle X} if for every...
abstract (L)-spaces. Banach space – Normed vectorspace that is complete Normed vector lattice Riesz space – Partially orderedvectorspace, ordered as a lattice...
point, the zero vector is called the origin. Adding a fixed vector to the elements of a linear subspace (vector subspace) of a vectorspace produces an affine...
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