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...

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...

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

In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite...

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

on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is called...

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

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

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...

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...

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...

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...

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

multiplication, it is a real vector space. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension...

order are comparable. The rational numbers as a linearly ordered set are a densely ordered set in this sense, as are the algebraic numbers, the real...

that is also maximum of the whole set. A well-ordered set as topological space is a first-countable space if and only if it has order type less than or...

order topology of an ordered vector space ( X , ≤ ) {\displaystyle (X,\leq )} is the finest locally convex topological vector space (TVS) topology on X...

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...

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...

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...

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...

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...

and a vector numerical value (unitless), often a Euclidean vector with magnitude and direction. For example, a position vector in physical space may be...

generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders. There are...

The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented...

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...

is bounded and relatively complemented. The lattice of subspaces of a vector space provide an example of a complemented lattice that is not, in general...

they overlap. In other words, a cyclically ordered set can be thought of as a locally linearly ordered space: an object like a manifold, but with order...