In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures...

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...

convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can...

in functional analysis and order theory, a topological vector lattice is a Hausdorff topological vector space (TVS) X {\displaystyle X} that has a partial...

put it more abstractly every seminormed vector space is a topological vector space and thus carries a topological structure which is induced by the semi-norm...

descriptions of redirect targets Ordered vector space – Vector space with a partial order Poset topology, a kind of topological space that can be defined from...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time,...

Ordered ring – ring with a compatible total orderPages displaying wikidata descriptions as a fallback Ordered topological vector space Ordered vector...

pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit...

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...

analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get...

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...

a topological vector lattice that is also a normed space whose unit ball is a solid set. Normed lattices are important in the theory of topological vector...

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

Topological vector space Metrizable topological vector space – A topological vector space whose topology can be defined by a metric Nuclear space – A generalization...

a topological module is a module over a topological ring such that scalar multiplication and addition are continuous. A topological vector space is a...

claimed to be homeomorphic to the topological quotient. Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback...

block form. A topological vector space (TVS) X , {\displaystyle X,} such as a Banach space, is said to be a topological direct sum of two vector subspaces...

ordinals and ω are discrete topological spaces, and no ordinal beyond that is discrete. The ordinal α is compact as a topological space if and only if α is either...

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...

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

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...

class of ordered topological vector spaces on which every positive linear form is necessarily continuous. This includes all topological vector lattices...

Ordered ring – ring with a compatible total orderPages displaying wikidata descriptions as a fallback Ordered topological vector space Ordered vector...

bilinear form Topological vector space, a blend of topological structure with the algebraic concept of a vector space A vector field is a vector-valued function...

be called the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear...

the case of topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article...

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...

In mathematics, a topological ring is a ring R {\displaystyle R} that is also a topological space such that both the addition and the multiplication are...