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- ...t]] of a countable inductive system <math>(X_n, i_{nm})</math> of [[Banach space]]s. ...nvex]] [[topological vector space]]s and each <math>X_n</math> is a Banach space. ...10 KB (1,494 words) - 02:17, 14 February 2024
- {{Short description|Type of topological vector space}} {{For|the space-filling curve|Hilbert curve}} ...128 KB (19,361 words) - 11:30, 28 February 2025
- {{Short description|Topological space}} ...inite [[subset]]s of ''X'': for a [[metric space]] ''X'' the [[topological space|topology]] is induced by the [[Hausdorff distance]]. The notion is named af ...5 KB (772 words) - 22:50, 7 October 2023
- ...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]]). ...6 KB (956 words) - 21:56, 12 August 2022
- [[File:Bing's_Dogbone.tiff|thumb|right|The first stage of the dogbone space construction.]] ...xt|Bing|1959}} showed that the [[Product topology|product]] of the dogbone space with <math>\R^1</math> is [[homeomorphic]] to <math>\R^4</math>. ...2 KB (298 words) - 03:16, 21 January 2023
- {{Short description|Property of topological space}} {{DISPLAYTITLE:G<sub>δ</sub> space}} ...5 KB (701 words) - 04:37, 12 January 2025
- {{Short description|Property of topological space}} ...(mathematics)|topology]], a '''Fréchet–Urysohn space''' is a [[topological space]] <math>X</math> with the property that for every subset <math>S \subseteq ...20 KB (3,113 words) - 01:11, 16 January 2024
- ...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}} ...5 KB (769 words) - 22:26, 7 March 2023
- In [[functional analysis]], a [[topological vector space]] (TVS) <math>X</math> is called '''ultrabornological''' if every [[bounded Let <math>X</math> be a [[topological vector space]] (TVS). ...6 KB (890 words) - 23:24, 2 November 2022
- ...-Frequency Analysis] by Karlheinz Gröchenig</ref> are a family of [[Banach space]]s defined by the behavior of the [[short-time Fourier transform]] with ...f> is identical to a certain modulation space and has become a widely used space of [[test function]]s for time-frequency analysis. ...4 KB (611 words) - 17:44, 4 January 2024
- ...mily <math>\mathcal{F}_1 \cup \mathcal{F}_2 \cup \cdots</math> covers the space. diameters that covers the space. Soon thereafter, ...5 KB (684 words) - 09:19, 26 January 2025
- {{Short description|Type of topological space}} ...atics, especially in topology, a '''stratified space''' is a [[topological space]] that admits or is equipped with a [[Stratification (mathematics)#In topol ...4 KB (584 words) - 09:09, 4 May 2024
- ...2. http://doi.org/10.1016/j.tics.2013.06.007</ref>{{rp|4}} In a conceptual space, ''points'' denote objects, and ''regions'' denote concepts. The theory of *[[Color space]] ...4 KB (532 words) - 22:44, 28 April 2024
- ...serve to generalize more elementary [[function space]]s such as [[Sobolev space]]s and are effective at measuring regularity properties of functions. ...{{math|''s'' {{=}} ''n'' + ''α''}} with {{math|0 < ''α'' ≤ 1}}. The Besov space <math>B^s_{p,q}(\mathbf{R})</math> contains all functions {{mvar|f}} such t ...3 KB (452 words) - 20:03, 25 January 2025
- In mathematics, and particularly [[functional analysis]], the '''Helly space''', named after [[Eduard Helly]], consists of all [[monotonically increasin Let the closed interval [0,1] be denoted simply by ''I''. We can form the space ''I<sup>I</sup>'' by taking the [[uncountable]] [[Cartesian product]] of cl ...2 KB (298 words) - 22:03, 24 November 2020
- {{Short description|Hilbert space of square-integrable holomorphic functions of n complex variables}} ...lso known as the '''Bargmann space''' or '''Bargmann–Fock space''', is the space of [[holomorphic function]]s ''F'' in ''n'' complex variables satisfying th ...13 KB (1,962 words) - 11:31, 13 December 2024
- ...<math>\mathcal C(X, \mathbb K)</math>, where <math>X</math> is a [[compact space]] and <math>\mathbb K</math> either the [[real numbers]] or the [[complex n ...988 bytes (138 words) - 03:26, 9 January 2025
- ...' (1951), pp. 411-429.</ref> are generalisations of the more familiar [[Lp space|<math>L^{p}</math> spaces]]. The Lorentz space on a [[measure space]] <math>(X, \mu)</math> is the space of complex-valued [[measurable function]]s <math>f</math> on ''X'' such tha ...9 KB (1,553 words) - 16:44, 5 September 2024
- ...tween" two other [[Banach space]]s. The main applications are in [[Sobolev space]]s, where spaces of functions that have a noninteger number of [[derivative ...{{mvar|p}} and {{mvar|q}}. In other words, {{math|''L<sup>r</sup>''}} is a space which is intermediate between {{math|''L<sup>p</sup>''}} and {{math|''L<sup ...35 KB (5,461 words) - 05:06, 11 February 2025
- ...lysis]], a '''Gelfand–Shilov space''' <math>S_{\alpha}^{\beta}</math> is a space of [[test function]]s for the theory of [[generalized function]]s, introduc {{DEFAULTSORT:Gelfand-Shilov space}} ...1 KB (154 words) - 22:28, 7 March 2023
Page text matches
- ...size of the output). The computation is generally done by means of a [[log-space transducer]]. == Log-space reductions == ...1 KB (156 words) - 12:33, 20 July 2022
- ...riants of topological properties|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. ...1 KB (183 words) - 03:50, 20 January 2023
- {{short description|Space formed by the ''n''-tuples of complex numbers}} ...ple]]s of [[complex number]]s, also known as ''[[complex vector]]s''. The space is denoted <math>\Complex^n</math>, and is the ''n''-fold [[Cartesian produ ...2 KB (289 words) - 17:10, 4 September 2024
- ...], more specifically in [[functional analysis]], a '''K-space''' is an [[F-space]] <math>V</math> such that every extension of F-spaces (or twisted sum) of ...l one<ref name="kalton">Kalton, N. J.; Peck, N. T.; Roberts, James W. An F-space sampler. London Mathematical Society Lecture Note Series, 89. Cambridge Uni ...1 KB (176 words) - 00:26, 3 November 2022
- ...Thus, every compact Hausdorff space is H-closed. The notion of an H-closed space has been introduced in 1924 by [[Pavel Alexandrov|P. Alexandroff]] and [[Pa * Every [[regular space|regular]] Hausdorff H-closed space is compact. ...1 KB (172 words) - 12:25, 16 January 2021
- ...[[real line]], the [[Cantor set]] and the [[Baire space (set theory)|Baire space]] are all effective Polish spaces. An effective Polish space is a complete separable metric space ''X'' with metric ''d'' such that there is a countable dense set ''C'' = (' ...1 KB (178 words) - 08:45, 6 March 2024
- {{Short description|On the dimension of vector space duals}} ...compute the exact dimension of any [[Vector space#Function space|function space]]. ...2 KB (304 words) - 07:53, 25 June 2024
- ...en the machine produces the group completion <math>BS \to K(S)</math>. The space <math>K(S)</math> may be described by the [[K-theory spectrum]] of ''S''. equivalence of all infinite loop space machines<ref>[https://www.ams.org/notices/199608/comm-thomason.pdf Charles ...1 KB (176 words) - 15:01, 19 July 2024
- ...ded countable union of [[equicontinuous]] subsets of its [[continuous dual space]] is again equicontinuous. This property is a generalization of [[quasibarrelled space]]s. ...4 KB (487 words) - 00:26, 3 November 2022
- ...motopy Theory - Fiber sequences]</ref> In other words, it is the [[mapping space]] from <math>(I, 0)</math> to <math>(X, *)</math>. ...ref> The maps from <math>I</math> to ''X'' are called free paths. The path space <math>PX</math> is then the pullback of <math>X^I \to X, \, \chi \mapsto \c ...2 KB (265 words) - 19:08, 12 December 2024
- ...'''abstract ''L''-space''', an '''AL-space''', or an '''abstract Lebesgue space''' is a [[Banach lattice]] <math>(X, \| \cdot \|)</math> whose norm is addi In [[probability theory]], it means the [[standard probability space]].<ref>{{citation |title=Stationary Stochastic Processes|author=Takeyuki Hi ...2 KB (309 words) - 00:10, 3 November 2022
- In the [[Mathematics|mathematical]] field of [[functional analysis]], the space '''bs''' consists of all infinite [[Sequence (mathematics)|sequences]] (''x ...ite. The set of such sequences forms a [[normed space]] with the [[vector space]] operations defined [[Componentwise operation|componentwise]], and the nor ...2 KB (273 words) - 03:11, 7 February 2025
- ...ded countable union of [[equicontinuous]] subsets of its [[continuous dual space]] is again equicontinuous. This property is a generalization of [[barrelled space]]s. ...4 KB (561 words) - 00:26, 3 November 2022
- ...on|acts]] trivially on the homotopy and homology of the universal covering space,<!-- what about principal fibration? --> though not all authors include the For example, any [[topological group]] is a simple space (provided it satisfies the condition on the homotopy type). ...1 KB (216 words) - 02:45, 8 March 2024
- ...bert C. ''A Non-Reflexive Banach Space Isometric With Its Second Conjugate Space.'' Proceedings of the National Academy of Sciences of the United States of ...dual]], while not being [[reflexive space|reflexive]]. Furthermore, James' space has a [[Schauder basis|basis]], while having no [[Schauder basis#Unconditio ...3 KB (387 words) - 05:00, 24 April 2024
- {{Short description|Mathematical space}} ...specially in [[real algebraic geometry]], a '''semialgebraic space''' is a space which is locally isomorphic to a [[semialgebraic set]]. ...1 KB (176 words) - 08:37, 8 May 2023
- ...c topology]], a '''Poincaré space''' is an ''n''-dimensional [[topological space]] with a distinguished element ''μ'' of its ''n''th [[homology group]] such | title=Poincaré space ...2 KB (224 words) - 00:04, 19 May 2024
- {{Short description|Space of bounded sequences}} ...[[functional analysis]], the space denoted by '''''c''''' is the [[vector space]] of all [[convergent sequence]]s <math>\left(x_n\right)</math> of [[real n ...2 KB (312 words) - 12:46, 12 March 2024
- [[File:Space cardioid.jpg|thumb|right|230px|A space cardioid introduction at [[Georgia Tech]]]] The '''space cardioid''' is a [[3-dimensional]] [[curve]] derived from the [[cardioid]]. ...832 bytes (105 words) - 01:49, 28 April 2024
- ...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 ...2 KB (351 words) - 00:44, 27 July 2024