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...he [[Mathematics|mathematical]] field of [[functional analysis]], [[Banach space]]s are among the most important objects of study. In other areas of [[math * The [[Asplund space]]s ...

...Grothendieck space is a Banach space for which a [[sequence]] in its dual space converges weak-* if and only if it converges weakly. Let <math>X</math> be a Banach space. Then the following conditions are equivalent: ...

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

{{short description|Space with one dimension}} ...e=ru|title=Пространство как математическое понятие|last=Гущин|first= Д. Д.|access-date=2015-06-06|publisher=fmclass.ru}}</ref> ...

...ed. Specifically, every weak Hausdorff space is a [[T1 space|T₁ space]].<ref>J.P. May, ''[http://www.math.uchicago.edu/~may/CONCISE/ConciseRevise ...of Hausdorff spaces. It is often used in tandem with [[compactly generated space]]s in [[algebraic topology]]. For that, see the [[category of compactly gen ...

...ontinuous dual <math>X^{\prime}</math>, {{mvar|X}} is called a '''Schwartz space''' if it satisfies any of the following equivalent conditions:{{sfn | Khale ...lete space|quasi-complete]] Schwartz space is a [[Montel space|semi-Montel space]]. ...

...eal-valued continuous function <math>g</math>. When dealing with [[compact space]]s, the two concepts are the same, but in general, the concepts are differe [[Rickart space]]s and the [[corona set]]s of locally compact σ-compact Hausdorff spaces ar ...

...generated space|compactly generated]] [[locally convex topological vector space]] <math>X</math> having a ''universal compact set'', i.e. a compact set <ma ...ace|stereotype]] and are in the stereotype duality relations with [[Banach space]]s:{{sfn|Akbarov|2003|p=220}}{{sfn|Akbarov|2009|p=467}} ...

.... They are named after E. G. Pytkeev, who proved in 1983 that [[sequential space]]s have this property.<ref>{{citation ...ons|volume=104|issue=2|pages=181–190|doi=10.1016/s0166-8641(99)00027-9|doi-access=free}}</ref> ...

{{Short description|Topological space}} {{DISPLAYTITLE:γ-space}} ...

...ology)|interior]]. Formally, if <math>X</math> is a [[Vector space|linear space]] then the quasi-relative interior of <math>A \subseteq X</math> is ...egacy.orie.cornell.edu/~aslewis/publications/92-partially-I.pdf|format=pdf|access-date=October 19, 2011|doi=10.1007/bf01581072}}</ref> ...

...Projectivization |url=https://mathworld.wolfram.com/Projectivization.html |access-date=2024-08-27 |website=mathworld.wolfram.com |language=en}}</ref> ...nse of [[algebraic geometry]] is one less than the dimension of the vector space {{math | ''V''}}. ...

...plete]] [[compactly generated space|compactly generated]] [[locally convex space]] <math>X</math> having a sequence of compact sets <math>K_n</math> such th ...ce|stereotype]] and are in the stereotype duality relations with [[Fréchet space]]s:{{sfn|Akbarov|2003|p=220}}{{sfn|Akbarov|2009|p=466}} ...

...= http://www-personal.umich.edu/~dsbaero/others/25-DoubleIntegrator.pdf | access-date = 2012-03-04 }}</ref> It models the dynamics of a simple mass in one-dimensional space under the effect of a time-varying force input <math>\textbf{u}</math>. ...

...e [[Schwartz space]] on a real [[vector space]], and is used to define the space of [[tempered representation|tempered distributions]] on a semisimple [[Lie The definition of the Schwartz space uses [[Harish-Chandra's Ξ function]] and his ''σ'' function. The ''σ'' func ...

...of their biduals (that is, the [[strong dual space]] of their strong dual space) are contained in the weak-* [[Closure (topology)|closure]] of some bounded ...note the [[strong dual]] of <math>X</math> (that is, the [[continuous dual space]] of <math>X</math> endowed with the [[strong dual|strong dual topology]]). ...

...]] &ndash; a '''Bochner-measurable function''' taking values in a [[Banach space]] is a [[function (mathematics)|function]] that equals almost everywhere th ...'' (or '''[[uniformly measurable]]''' in case that the Banach space is the space of continuous [[linear operator]]s between Banach spaces). ...

...g space transducer (LST)''' is a type of [[Turing machine]] used for [[log-space reduction]]s. A log space transducer, <math>M</math>, has three tapes: ...

...onvex space |url=https://ncatlab.org/nlab/show/convex+space |website=nLab |access-date=3 April 2023}}</ref><ref>{{cite arXiv |last1=Fritz |first1=Tobias |tit A convex space can be defined as a set <math>X</math> equipped with a binary convex combin ...

...y)|url=https://plato.stanford.edu/entries/set-theory/basic-set-theory.html|access-date=2020-08-12|website=plato.stanford.edu}}</ref> of which there are uncou ...rdinal in nLab|url=https://ncatlab.org/nlab/show/first+uncountable+ordinal|access-date=2020-08-12|website=ncatlab.org}}</ref> ...