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- In [[mathematics]], a [[topological group]] <math>G</math> is called the '''topological direct sum'''<ref>E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol is a topological isomorphism, meaning that it is a [[homeomorphism]] and a [[group isomorphi ...3 KB (430 words) - 01:29, 11 May 2022
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- {{Short description|Restriction on topological groups in mathematics}} ...ath> An abbreviation '"'''NSS'''"' is sometimes used. A basic example of a topological group with no small subgroup is the [[general linear group]] over the compl ...1 KB (157 words) - 02:52, 12 August 2023
- ...ept of a [[topological group]]; all topological groups are semitopological groups but the [[Converse (logic)|converse]] does not hold. A semitopological group <math>G</math> is a topological space that is also a [[Group (mathematics)|group]] such that ...3 KB (398 words) - 14:48, 21 February 2025
- ...[[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 === ...1 KB (216 words) - 02:45, 8 March 2024
- ...tics)|measures]] is an abstract setting and are often closely related to [[topological group]]s. == Topological groups as measurable groups == ...2 KB (378 words) - 00:32, 2 October 2020
- ...discontinuous group''' is a mathematical concept relating to mappings in [[topological space]]. ...l Ludwig Siegel|editor-surname1= Annals of Mathematics|title=Discontinuous groups|volume=44|issue=4|at=pp. 674−689|date=1943 ...1 KB (177 words) - 09:24, 18 November 2024
- In [[mathematics]], a [[topological group]] <math>G</math> is called the '''topological direct sum'''<ref>E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol is a topological isomorphism, meaning that it is a [[homeomorphism]] and a [[group isomorphi ...3 KB (430 words) - 01:29, 11 May 2022
- ...m/pdf?fm178-3-05 | doi-access=free }}</ref> Every extension of topological groups is therefore a [[group extension]]. ==Classification of extensions of topological groups== ...6 KB (888 words) - 23:42, 5 February 2025
- ...en a discrete topology, then <math>M</math> becomes a [[Topological module|topological <math>A</math>-module]] with respect to a linear topology. ...spaces ''over discrete fields'', analogous to the class of locally convex topological vector spaces over the normed fields of real or complex numbers in function ...2 KB (345 words) - 11:49, 28 November 2024
- In [[group theory]], a '''balanced group''' is a [[topological group]] whose left and right [[uniform space|uniform structres]] coincide. A topological group <math>G</math> is said to be '''balanced''' if it satisfies the follo ...3 KB (468 words) - 09:15, 18 November 2024
- ...]], a '''Banach bundle''' is a [[fiber bundle]] over a [[Topological space|topological]] [[Hausdorff space]], such that each fiber has the structure of a [[Banach ...is a tuple <math>\mathfrak{B} = (B, \pi)</math>, where <math>B</math> is a topological Hausdorff space, and <math>\pi\colon B\to X</math> is a [[continuous functi ...2 KB (327 words) - 08:12, 31 May 2022
- ...p]]s. Equivalently, a group is called '''prosolvable''', if, viewed as a [[topological group]], every [[open neighborhood]] of the identity contains a [[normal su [[Category:Properties of groups]] ...2 KB (280 words) - 22:04, 4 May 2024
- ...module''' consists of<ref>{{Citation|title=Representation Theory of Finite Groups and Associative Algebras|year=1962|last1=Curtis|last2=Reiner|first1=Charles ==Topological groups== ...6 KB (938 words) - 00:21, 22 January 2025
- ...rst1=N.H. |last2=Ostaszewski |first2=A.J. |title=Normed versus topological groups: Dichotomy and duality |journal=Dissertationes Mathematicae |date=2010 |vol | title = A characterization of free abelian groups ...2 KB (264 words) - 16:02, 22 September 2023
- In mathematics, '''Topological Hochschild homology''' is a topological refinement of [[Hochschild homology]] which rectifies some technical issues ...use |first1=Achim |last2=Nikolaus |first2=Thomas |date= |title=Lectures on Topological Hochschild Homology and Cyclotomic Spectra |url=https://www.uni-muenster.de ...4 KB (607 words) - 15:48, 3 October 2024
- In [[topology]], a branch of mathematics, a [[topological space]] ''X'' is said to be '''simply connected at infinity''' if for any [ [[Category:Properties of topological spaces]] ...1 KB (200 words) - 15:34, 2 October 2024
- {{Short description|special kind of topological group - translation from the German Wikipedia}} A '''pro-Lie group''' is in [[mathematics]] a [[topological group]] that can be written in a certain sense as a limit of [[Lie group]]s ...7 KB (985 words) - 12:46, 20 February 2025
- ...Product on the homology of a topological space induced by a product on the topological space}} ...ematics)|homology]] of a [[topological space]] induced by a product on the topological space. Special cases include the Pontryagin product on the homology of an [ ...3 KB (519 words) - 03:13, 28 September 2024
- ...nction (topology)|continuous map]] from a [[topological space]] ''X'' to a topological space ''Y'' induces a [[group homomorphism]] from the [[fundamental group]] ...(e.g.) the [[category of topological spaces]] to (e.g.) the [[category of groups]] or [[category of rings|rings]]. This means that each space is associated ...10 KB (1,490 words) - 03:09, 28 September 2024
- ...der to solve some technical problems of doing [[homological algebra]] on [[topological group]]s. ...ical group|topological abelian groups]], the category of condensed abelian groups is an [[abelian category]], which allows for the use of tools from [[homolo ...7 KB (1,022 words) - 01:47, 28 January 2025
- {{Short description|Totally disconnected topological space}} In [[mathematics]], '''Erdős space''' is a [[topological space]] named after [[Paul Erdős]], who described it in 1940.<ref name="erd ...2 KB (370 words) - 20:20, 15 April 2024