Search results

{{Short description|Subset T of a topological vector space X where the linear span of T is a dense subset of X}} ...re specifically 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 ...

...[[mathematics]], a '''simple space''' is a [[connected space|connected]] [[topological space]] that has a homotopy type of a [[CW complex]] and whose [[fundamenta === Topological groups === ...

...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."< ...

...|pairwise Hausdorff]], and [[bitopological space#Bitopological variants of topological properties|pairwise zero-dimensional]]. Pairwise Stone spaces are a bitopological version of the [[Stone space]]s. ...

...thematics, a '''hypocontinuous''' is a condition on [[bilinear map]]s of [[topological vector space]]s that is weaker than continuity but stronger than [[separate 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> ...

...th>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 * {{Narici Beckenstein Topological Vector Spaces|edition=2}} <!-- {{sfn|Narici|Beckenstein|2011|p=}} --> ...

...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. ...

{{Short description|A topological vector space in which every closed and bounded subset is complete}} ...Wilansky | 2013 | p=73}} if every [[closed set|closed]] and [[Bounded set (topological vector space)|bounded]] subset is [[complete space|complete]].{{sfn | Schae ...

...regularly ordered vector space is an important property in the theory of [[topological vector lattice]]s. ...erings of subspaces, products, and direct sums of regularly ordered vector spaces are again regularly ordered.{{sfn|Schaefer|Wolff|1999|pp=222–225}} ...

{{Short description|Categorical treatment of topological spaces}} {{Other uses|Topological concrete category}} ...

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 th * {{annotated link|Topologies on spaces of linear maps}} ...

...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]]. ...

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

{{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< ...

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

...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 ...

...c topology]], a pair <math>(X,A)</math> is shorthand for an inclusion of [[topological space]]s <math>i\colon A \hookrightarrow X</math>. Sometimes <math>i</math ...(topology)|quotient space]] of {{math|''X''}} by {{math|''A''}}. Pairs of spaces occur centrally in [[relative homology]],<ref name="hatcher">{{cite book | ...

...graph theorem]] is valid for [[linear map]]s defined on and valued in most spaces encountered in analysis.{{sfn|Trèves|2006|p=549}} ...an space]] as well as many other spaces that occur in analysis are Souslin spaces. The Borel graph theorem states:{{sfn|Trèves|2006|p=549}} ...

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

...discontinuous group''' is a mathematical concept relating to mappings in [[topological space]]. .../math>, <math>x\in G</math>, be an open continuous representation of the [[topological group]] <math>G</math> as a [[transitive relation|transitive]] group of [[h ...