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{{Short description|Subset T of a topological vector space X where the linear span of T is a dense subset of X}} ...lly in [[functional analysis]], a subset <math>T</math> of a [[topological vector space]] <math>X</math> is said to be a '''total''' subset of <math>X</math> ...

...en a discrete topology, then <math>M</math> becomes a [[Topological module|topological <math>A</math>-module]] with respect to a linear topology. ...rete fields'', analogous to the class of locally convex topological vector spaces over the normed fields of real or complex numbers in functional analysis."< ...

...der theory]] and [[functional analysis]], an element <math>x</math> of a [[vector lattice]] <math>X</math> is called a '''weak order unit''' in <math>X</math ...is a [[Separable space|separable]] [[Fréchet space|Fréchet]] [[topological vector lattice]] then the set of weak order units is dense in the positive cone of ...

...specifically in [[order theory]] and [[functional analysis]], an [[ordered vector space]] <math>X</math> is said to be '''regularly ordered''' and its order ...dered vector space is an important property in the theory of [[topological vector lattice]]s. ...

...0</math> for all <math>f \in T,</math> then <math>x = 0</math> is the zero vector.<ref name=Klauder2010>{{cite book|last1=Klauder|first1=John R.|title=A Mode In a more general setting, a subset <math>T</math> of a [[topological vector space]] <math>X</math> is a total set or '''fundamental set''' if the [[lin ...

{{Short description|A topological vector space in which every closed and bounded subset is complete}} ...013 | p=73}} if every [[closed set|closed]] and [[Bounded set (topological vector space)|bounded]] subset is [[complete space|complete]].{{sfn | Schaefer | W ...

...'''hypocontinuous''' is a condition on [[bilinear map]]s of [[topological vector space]]s that is weaker than continuity but stronger than [[separate contin If <math>X</math>, <math>Y</math> and <math>Z</math> are [[topological vector space]]s then a [[bilinear map]] <math>\beta: X\times Y\to Z</math> is call ...

...amily of sets|family]] <math>\mathcal{G}</math> of subsets a [[topological vector space]] (TVS) <math>X</math> is said to be '''saturated''' if <math>\mathca The set of all [[Von Neumann bounded|bounded]] subsets of a [[topological vector space]] is a saturated family. ...

...K-space''' is an [[F-space]] <math>V</math> such that every extension of F-spaces (or twisted sum) of the form The [[Lp space|<math>\ell^p</math> spaces]] for <math>0< p < 1</math> are K-spaces,<ref name="kalton"/> as are all finite dimensional [[Banach space]]s. ...

...ft(x_i\right)_{i=1}^{\infty}</math> in a [[Ordered vector space|preordered vector space]] <math>X</math> (that is, <math>x_i \geq 0</math> for all <math>i</m * {{annotated link|Ordered topological vector space}} ...

...a property similar to the definition of [[totally bounded]] subsets. These spaces were introduced by [[Alexander Grothendieck]]. The [[strong dual space]] of a [[Complete topological vector space|complete]] Schwartz space is an [[ultrabornological space]]. ...

{{short description|Partially ordered topological space}} ...017/CBO9780511542725|isbn=9780521803380 }}</ref> (or '''pospace''') is a [[topological space]] <math>X</math> equipped with a closed [[partial order]] <math>\leq< ...

...nctional analysis]], an element <math>x</math> of an [[ordered topological vector space]] <math>X</math> is called a '''quasi-interior point''' of the positi ...lly convex topological vector space|locally convex]] [[ordered topological vector space]] whose positive cone <math>C</math> is a complete and total subset o ...

{{Short description|Property of subsets of ordered vector spaces}} ...ory]] and [[functional analysis]], a subset <math>A</math> of an [[ordered vector space]] is said to be '''order complete''' in <math>X</math> if for every n ...

...athematics]], a '''quasi-ultrabarrelled space''' is a [[topological vector spaces]] (TVS) for which every [[Barrelled set|bornivorous ultrabarrel]] is a [[ne ...1=Alex P. | last2=Robertson | first2= Wendy J. | title= Topological vector spaces | series=Cambridge Tracts in Mathematics | volume=53 | year=1964 | publishe ...

.../math> that has a [[partial order]] <math>\,\leq\,</math> making it into [[vector lattice]] that possesses a neighborhood base at the origin consisting of [[ Ordered vector lattices have important applications in [[spectral theory]]. ...

In [[functional analysis]], a [[topological vector space]] (TVS) is said to be '''countably quasi-barrelled''' if every strong ...sequently σ-quasi-barrelled spaces) that are not countably quasi-barrelled spaces.{{sfn | Khaleelulla | 1982 | pp=28-63}} ...

...t|Tensor product of vector spaces]], an operation on [[Vector space|vector spaces]] (the original tensor product) ...ct of matrices (or vectors), which satisfies all the properties for vector spaces and allows a concrete representation ...

...f [[mathematics]], an '''ultrabarrelled space''' is a [[topological vector spaces]] (TVS) for which every ultrabarrel is a [[Neighbourhood (topology)|neighbo * {{Husain Khaleelulla Barrelledness in Topological and Ordered Vector Spaces}} <!-- {{sfn|Husain|Khaleelulla|1978|p=}} --> ...

In [[functional analysis]], a [[topological vector space]] (TVS) is said to be '''countably barrelled''' if every weakly bound ...r, there exist [[Semi-reflexive space|semi-reflexive]] countably barrelled spaces that are not barrelled.{{sfn | Khaleelulla | 1982 | pp=28-63}} ...