In mathematics, a tubular neighborhood of a submanifold of a smooth manifold is an open set around it resembling the normal bundle. The idea behind a tubular neighborhood can be explained in a simple example. Consider a smooth curve in the plane without self-intersections. On each point on the curve draw a line perpendicular to the curve. Unless the curve is straight, these lines will intersect among themselves in a rather complicated fashion. However, if one looks only in a narrow band around the curve, the portions of the lines in that band will not intersect, and will cover the entire band without gaps. This band is a tubular neighborhood.
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| - Tubulare Umgebung (de)
- Teorema dell'intorno tubolare (it)
- Voisinage tubulaire (fr)
- 관상 주변 (ko)
- Tubular neighborhood (en)
- Трубчатая окрестность (ru)
- Трубчастий окіл (uk)
- 管状邻域 (zh)
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| rdfs:comment
| - In der Mathematik ist die tubulare Umgebung oder Tubenumgebung ein häufig verwendetes technisches Hilfsmittel der Differentialtopologie. (de)
- En géométrie différentielle, un voisinage tubulaire d'une sous-variété S d'une variété différentielle M est un ouvert de M, qui contient S et « ressemble à » son fibré normal. (fr)
- In geometria, il teorema dell'intorno tubolare è un importante strumento della topologia differenziale, utile in presenza di una varietà differenziabile contenuta in un'altra varietà di dimensione più grande. Si tratta di uno dei primi risultati topologici in cui è necessaria la struttura differenziabile: il teorema può non essere valido infatti nell'ambito delle varietà topologiche. (it)
- 미분기하학에서, 관상 주변(管狀周邊, 영어: tubular neighbo(u)rhood)은 어떤 의 근방과, 이 부분 다양체의 법다발 사이의 위상 동형이다. (ko)
- Трубчатая окрестность подмногообразия в многообразии — это открытое множество, окружающее подмногообразие и локально устроенное подобно нормальному расслоению. (ru)
- Трубчастий окіл підмноговиду в многовиді — це відкрита множина, що оточує підмноговид і локально влаштована подібно нормальному розшаруванню. (uk)
- 在数学中，一个光滑流形的子流形的管状邻域是它周围的一个开集，与法丛类似。 管状邻域的想法可以用一个简单的例子说明。考虑平面内一个没有自交的光滑曲线。在曲线的每一个点处作一条与这个曲线垂直的直线。这些直线之间会以一种很复杂的形式相交，除非这条曲线是直的。然而，如果只观察临近曲线的一个狭窄的条带，这些直线在条带内的部分不会相交，并会没有缝隙地覆盖这个条带。这个条带就是一个管状邻域。 一般地，令S为流形M的一个子流形，令N为在M上S的法丛。这里S扮演曲线的角色，M扮演包含曲线的空间的角色。考虑自然映射 建立起N的N0与M的一个子流形S之间的双射关系。关于值在M中的全部法丛N的这个映射的一个外延j，使j(N)是M上的一个开集，并且j是N与j(N)的一个同胚，称作管状邻域。 (zh)
- In mathematics, a tubular neighborhood of a submanifold of a smooth manifold is an open set around it resembling the normal bundle. The idea behind a tubular neighborhood can be explained in a simple example. Consider a smooth curve in the plane without self-intersections. On each point on the curve draw a line perpendicular to the curve. Unless the curve is straight, these lines will intersect among themselves in a rather complicated fashion. However, if one looks only in a narrow band around the curve, the portions of the lines in that band will not intersect, and will cover the entire band without gaps. This band is a tubular neighborhood. (en)
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| - In der Mathematik ist die tubulare Umgebung oder Tubenumgebung ein häufig verwendetes technisches Hilfsmittel der Differentialtopologie. (de)
- En géométrie différentielle, un voisinage tubulaire d'une sous-variété S d'une variété différentielle M est un ouvert de M, qui contient S et « ressemble à » son fibré normal. (fr)
- In mathematics, a tubular neighborhood of a submanifold of a smooth manifold is an open set around it resembling the normal bundle. The idea behind a tubular neighborhood can be explained in a simple example. Consider a smooth curve in the plane without self-intersections. On each point on the curve draw a line perpendicular to the curve. Unless the curve is straight, these lines will intersect among themselves in a rather complicated fashion. However, if one looks only in a narrow band around the curve, the portions of the lines in that band will not intersect, and will cover the entire band without gaps. This band is a tubular neighborhood. In general, let S be a submanifold of a manifold M, and let N be the normal bundle of S in M. Here S plays the role of the curve and M the role of the plane containing the curve. Consider the natural map which establishes a bijective correspondence between the zero section of N and the submanifold S of M. An extension j of this map to the entire normal bundle N with values in M such that is an open set in M and j is a homeomorphism between N and is called a tubular neighbourhood. Often one calls the open set rather than j itself, a tubular neighbourhood of S, it is assumed implicitly that the homeomorphism j mapping N to T exists. (en)
- In geometria, il teorema dell'intorno tubolare è un importante strumento della topologia differenziale, utile in presenza di una varietà differenziabile contenuta in un'altra varietà di dimensione più grande. Si tratta di uno dei primi risultati topologici in cui è necessaria la struttura differenziabile: il teorema può non essere valido infatti nell'ambito delle varietà topologiche. (it)
- 미분기하학에서, 관상 주변(管狀周邊, 영어: tubular neighbo(u)rhood)은 어떤 의 근방과, 이 부분 다양체의 법다발 사이의 위상 동형이다. (ko)
- Трубчатая окрестность подмногообразия в многообразии — это открытое множество, окружающее подмногообразие и локально устроенное подобно нормальному расслоению. (ru)
- Трубчастий окіл підмноговиду в многовиді — це відкрита множина, що оточує підмноговид і локально влаштована подібно нормальному розшаруванню. (uk)
- 在数学中，一个光滑流形的子流形的管状邻域是它周围的一个开集，与法丛类似。 管状邻域的想法可以用一个简单的例子说明。考虑平面内一个没有自交的光滑曲线。在曲线的每一个点处作一条与这个曲线垂直的直线。这些直线之间会以一种很复杂的形式相交，除非这条曲线是直的。然而，如果只观察临近曲线的一个狭窄的条带，这些直线在条带内的部分不会相交，并会没有缝隙地覆盖这个条带。这个条带就是一个管状邻域。 一般地，令S为流形M的一个子流形，令N为在M上S的法丛。这里S扮演曲线的角色，M扮演包含曲线的空间的角色。考虑自然映射 建立起N的N0与M的一个子流形S之间的双射关系。关于值在M中的全部法丛N的这个映射的一个外延j，使j(N)是M上的一个开集，并且j是N与j(N)的一个同胚，称作管状邻域。 (zh)
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