End (topology) (original) (raw)
In der Mathematik sind die Enden eines topologischen Raumes anschaulich gesprochen die Zusammenhangskomponenten des „Randes im Unendlichen“. Formal definiert werden sie als Äquivalenzklassen von Komplementen kompakter Mengen.
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| dbo:abstract | In der Mathematik sind die Enden eines topologischen Raumes anschaulich gesprochen die Zusammenhangskomponenten des „Randes im Unendlichen“. Formal definiert werden sie als Äquivalenzklassen von Komplementen kompakter Mengen. (de) In topology, a branch of mathematics, the ends of a topological space are, roughly speaking, the connected components of the "ideal boundary" of the space. That is, each end represents a topologically distinct way to move to infinity within the space. Adding a point at each end yields a compactification of the original space, known as the end compactification. The notion of an end of a topological space was introduced by Hans Freudenthal. (en) En mathématiques, un bout d'un espace topologique est de manière informelle une « composante connexe à l'infini » de cet espace. Dans les bons cas, ajouter un point pour chaque bout induit une compactification de dimension nulle de l'espace, on parle de compactification par les bouts ou Endenkompaktifiezierung en allemand, ou encore end compactification en anglais. Un bout d'un groupe topologique est une classe d'équivalence de bouts de l'espace topologique sous-jacent pour une relation d'équivalence liée à l'action du groupe. (fr) 일반위상수학에서, 끝(영어: end)은 대략 어떤 위상 공간의 "경계"의 "연결 성분"을 뜻한다. 구체적으로, 점점 더 큰 콤팩트 집합을 잘라냈을 때 남는 연결 성분들의 이다. (ko) 数学の一分野である位相空間論において、位相空間の端点（たんてん、英: end; 端）全体の成す集合は、大雑把に言えばその空間の「想像上の境界」(“ideal boundary”) の連結成分である。つまり、各端点はその空間の中で無限遠へ行くための位相的に相異なる方法を示すものになる。各端にそれぞれひとつの端点を加えるという操作は、もとの空間の端コンパクト化 (end compactification) と呼ばれるコンパクト化を導く。 (ja) Конец топологического пространства — грубо говоря, компонента связности его «идеальной границы».То есть, каждый конец представляет собой способ двигаться к бесконечности в пространстве. Добавление точки на каждом конце даёт компактификацию исходного пространства, известную как конечная компактификация. (ru) |
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| dbp:authorlink | Hans Freudenthal (en) |
| dbp:first | Hans (en) |
| dbp:last | Freudenthal (en) |
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| dbp:year | 1931 (xsd:integer) |
| dct:subject | dbc:Compactification_(mathematics) dbc:Properties_of_topological_spaces dbc:General_topology |
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| rdfs:comment | In der Mathematik sind die Enden eines topologischen Raumes anschaulich gesprochen die Zusammenhangskomponenten des „Randes im Unendlichen“. Formal definiert werden sie als Äquivalenzklassen von Komplementen kompakter Mengen. (de) In topology, a branch of mathematics, the ends of a topological space are, roughly speaking, the connected components of the "ideal boundary" of the space. That is, each end represents a topologically distinct way to move to infinity within the space. Adding a point at each end yields a compactification of the original space, known as the end compactification. The notion of an end of a topological space was introduced by Hans Freudenthal. (en) En mathématiques, un bout d'un espace topologique est de manière informelle une « composante connexe à l'infini » de cet espace. Dans les bons cas, ajouter un point pour chaque bout induit une compactification de dimension nulle de l'espace, on parle de compactification par les bouts ou Endenkompaktifiezierung en allemand, ou encore end compactification en anglais. Un bout d'un groupe topologique est une classe d'équivalence de bouts de l'espace topologique sous-jacent pour une relation d'équivalence liée à l'action du groupe. (fr) 일반위상수학에서, 끝(영어: end)은 대략 어떤 위상 공간의 "경계"의 "연결 성분"을 뜻한다. 구체적으로, 점점 더 큰 콤팩트 집합을 잘라냈을 때 남는 연결 성분들의 이다. (ko) 数学の一分野である位相空間論において、位相空間の端点（たんてん、英: end; 端）全体の成す集合は、大雑把に言えばその空間の「想像上の境界」(“ideal boundary”) の連結成分である。つまり、各端点はその空間の中で無限遠へ行くための位相的に相異なる方法を示すものになる。各端にそれぞれひとつの端点を加えるという操作は、もとの空間の端コンパクト化 (end compactification) と呼ばれるコンパクト化を導く。 (ja) Конец топологического пространства — грубо говоря, компонента связности его «идеальной границы».То есть, каждый конец представляет собой способ двигаться к бесконечности в пространстве. Добавление точки на каждом конце даёт компактификацию исходного пространства, известную как конечная компактификация. (ru) |
| rdfs:label | Ende (Topologie) (de) End (topology) (en) Bout (topologie) (fr) 끝 (위상수학) (ko) 端点 (ja) Конец топологического пространства (ru) |
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