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

...himedean ordered]] and the [[Order dual (functional analysis)|order dual]] of <math>X</math> distinguishes points in <math>X</math>.{{sfn|Schaefer|Wolff| ...regularly ordered vector space is an important property in the theory of [[topological vector lattice]]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 ...

{{short description|Partially ordered topological space}} ...ose graph <math>\{(x, y) \in X^2 \mid x \leq y\}</math> is a closed subset of <math>X^2</math>. ...

...a property similar to the definition of [[totally bounded]] subsets. These spaces were introduced by [[Alexander Grothendieck]]. ...e}</math>, {{mvar|X}} is called a '''Schwartz space''' if it satisfies any of the following equivalent conditions:{{sfn | Khaleelulla | 1982 | p=32}} ...

...'' if every strongly bounded countable union of [[equicontinuous]] subsets of its [[continuous dual space]] is again equicontinuous. This property is a generalization of [[quasibarrelled space]]s. ...

...|bornivorous ultrabarrel]] is a [[neighbourhood (topology)|neighbourhood]] of the origin. ...} \right)_{i=1}^{\infty}</math> of closed balanced and bornivorous subsets of ''X'' such that ''B''_''i''+1 + ''B''_''i''+1 &sube; '' ...

...th>; that is, if the linear span of <math>[0, x]</math> is a dense subset of <math>X.</math>{{sfn|Schaefer|Wolff|1999|pp=234–242}} == Properties == ...

...d''' if every weakly bounded countable union of [[equicontinuous]] subsets of its [[continuous dual space]] is again equicontinuous. This property is a generalization of [[barrelled space]]s. ...

...nment of some [[Closed set|closed]] [[Isolated point|discrete]] [[subset]] of the space. ...ns an open neighborhood to each element in the set. More formally, given a topological space <math>X</math>. An open neighborhood assignment is a function <math>f ...

...or which every ultrabarrel is a [[Neighbourhood (topology)|neighbourhood]] of the origin. ...{\infty}</math> of closed balanced and [[absorbing set|absorbing]] subsets of <math>X</math> such that <math>B_{i+1} + B_{i+1} \subseteq B_i</math> for a ...

{{short description|Topological space mathematics}} [[File:Alexandroff plank.svg|thumb|350px|Diagram of Alexandroff plank]] ...

...l]], and [[Symmetric relation|symmetric]] ([[up to]] some appropriate kind of [[Mathematical structure|structural]] equivalence). ...t|Tensor product of vector spaces]], an operation on [[Vector space|vector spaces]] (the original tensor product) ...

{{Short description|Property of subsets of ordered vector spaces}} ...math>' and the [[infimum]] <math>\inf S</math> both exist and are elements of <math>A.</math> ...

...tained in the weak-* [[Closure (topology)|closure]] of some bounded subset of the bidual. ...[[strong dual]] of <math>X</math> (that is, the [[continuous dual space]] of <math>X</math> endowed with the [[strong dual|strong dual topology]]). ...

...ctor lattice]] that possesses a neighborhood base at the origin consisting of [[solid set]]s.{{sfn|Schaefer|Wolff|1999|pp=234–242}} If <math>X</math> is a vector lattice and an [[ordered topological vector space]] that is a [[Fréchet space]] in which the positive cone is a ...

A [[locally convex]] [[topological vector space]] (TVS) <math>X</math> is '''''B''-complete''' or a '''Ptak sp ...th> will be a [[Locally convex topological vector space|locally convex]] [[topological vector space]] (TVS). ...

{{Short description|Topological space arising from a usual graph}} ...math> with the point associated to <math>y</math>. That is, as topological spaces, graphs are exactly the [[simplicial complex|simplicial 1-complex]]es and a ...

...ne <math>C := \left\{ x \in X : x \geq 0\right\}</math> is a closed subset of ''X''.{{sfn | Schaefer | Wolff | 1999 | pp=222–225}} ...t)</math> is the [[Cone-saturated|''C''-saturated]] hull of a subset ''U'' of ''X''.{{sfn | Schaefer | Wolff | 1999 | pp=215–222}} ...

...ogical vector space)|bounded]] [[Barreled space|barrel]] is a neighborhood of the origin.{{sfn|Schaefer|Wolff|1999|p=142}} ...barrelled set in the space is a [[Neighbourhood (topology)|neighbourhood]] of the origin. ...