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- Tubular_neighborhood abstract "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 mapwhich establishes a bijective correspondence between the zero section N0 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 j(N) is an open set in M and j is a homeomorphism between N and j(N) is called a tubular neighbourhood.Often one calls the open set T=j(N), rather than j itself, a tubular neighbourhood of S, it is assumed implicitly that the homeomorphism j mapping N to T exists.".
- Tubular_neighborhood thumbnail Tubular_neighborhood.png?width=300.
- Tubular_neighborhood wikiPageID "3192042".
- Tubular_neighborhood wikiPageRevisionID "549604596".
- Tubular_neighborhood hasPhotoCollection Tubular_neighborhood.
- Tubular_neighborhood subject Category:Geometric_topology.
- Tubular_neighborhood subject Category:Manifolds.
- Tubular_neighborhood type Artifact100021939.
- Tubular_neighborhood type Conduit103089014.
- Tubular_neighborhood type Manifold103717750.
- Tubular_neighborhood type Manifolds.
- Tubular_neighborhood type Object100002684.
- Tubular_neighborhood type Passage103895293.
- Tubular_neighborhood type PhysicalEntity100001930.
- Tubular_neighborhood type Pipe103944672.
- Tubular_neighborhood type Tube104493505.
- Tubular_neighborhood type Way104564698.
- Tubular_neighborhood type Whole100003553.
- Tubular_neighborhood type YagoGeoEntity.
- Tubular_neighborhood type YagoPermanentlyLocatedEntity.
- Tubular_neighborhood comment "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.".
- Tubular_neighborhood label "Teorema dell'intorno tubolare".
- Tubular_neighborhood label "Tubular neighborhood".
- Tubular_neighborhood label "Tubulare Umgebung".
- Tubular_neighborhood label "Трубчатая окрестность".
- Tubular_neighborhood label "管状邻域".
- Tubular_neighborhood sameAs Tubulare_Umgebung.
- Tubular_neighborhood sameAs Teorema_dell'intorno_tubolare.
- Tubular_neighborhood sameAs m.08y85p.
- Tubular_neighborhood sameAs Q1141920.
- Tubular_neighborhood sameAs Q1141920.
- Tubular_neighborhood sameAs Tubular_neighborhood.
- Tubular_neighborhood wasDerivedFrom Tubular_neighborhood?oldid=549604596.
- Tubular_neighborhood depiction Tubular_neighborhood.png.
- Tubular_neighborhood isPrimaryTopicOf Tubular_neighborhood.
