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In mathematics, a compact (topological) group is a topological group whose topology is compact. Compact groups are a natural generalization of finite groups with the discrete topology and have properties that carry over in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory. In the following we will assume all groups are Hausdorff spaces.

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  • Grup compacte
  • Compact group
  • Groupe compact
  • コンパクト群
  • Compacte groep
  • Grupo compacto
  • 緊群
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  • En matemàtiques, un grup (topològic, sovint sobreentès) compacte és un grup la topologia del qual és compacta. Els grups compactes són una generalització natural dels grups finits amb topologia discreta. D'ara endavant, assumirem que tots els grups són espais de Hausdorff.
  • In mathematics, a compact (topological) group is a topological group whose topology is compact. Compact groups are a natural generalization of finite groups with the discrete topology and have properties that carry over in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory. In the following we will assume all groups are Hausdorff spaces.
  • En mathématiques, et plus particulièrement en analyse harmonique abstraite, un groupe compact est un groupe topologique dont l'espace topologique sous-jacent est compact. Les groupes compacts sont des groupes unimodulaires, dont la compacité simplifie l'étude. Ces groupes comprennent notamment les groupes finis et les groupes de Lie compacts. Tout groupe compact est limite projective de groupes de Lie compacts.
  • 数学において、コンパクト(位相)群とは位相がコンパクトな位相群である。コンパクト群は離散位相をいれた有限群の自然な一般化であり、重要な性質が持ち越される。コンパクト群は群作用と表現論に関してよく理解された理論を持つ。 以下では常に群はハウスドルフと仮定する。
  • In de groepentheorie, een deelgebied van de wiskunde, is een compacte groep een topologische groep, waarvan de topologie compact is. Compacte groepen zijn natuurlijke generalisaties van eindige groepen met discrete topologie en hebben eigenschappen die in belangrijke mate daarmee overeenkomen. Compacte groepen hebben een goed begrepen theorie metr betrekking tot groepsbewerkingen en de representatietheorie In het hieronderstaande wordt aangenomen dat alle groepen voldoen aan de hausdorff-eigenschap.
  • Em matemática, um grupo (frequentemente entendido como topológico) compacto é um grupo topológico cuja topologia é compacta. Grupos compactos são uma generalização natural de grupos finitos com a topologia discreta e tendo propriedades que implicam uma forma significativa. Grupos compactos tem uma teoria bem compreendida, em relação aos grupos de ação e teoria da representação. A seguir assumiremos que todos os grupos tratados são de Hausdorff.
  • 在數學中,緊群是其拓撲為緊緻的的拓撲群。緊群是帶有離散拓撲的有限群的自然推廣,并以顯著方式延續了一些性質。緊群的理論已被人们深入研究,與群作用和群表示論有關。 下面我們假定所有群都是豪斯多夫空間,因為這個覆蓋了所有有價值的情況。
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