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Vector_bundle abstract "In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X.The simplest example is the case that the family of vector spaces is constant, i.e., there is a fixed vector space V such that V(x) = V for all x in X: in this case there is a copy of V for each x in X and these copies fit together to form the vector bundle X × V over X. Such vector bundles are said to be trivial. A more complicated (and prototypical) class of examples are the tangent bundles of smooth (or differentiable) manifolds: to every point of such a manifold we attach the tangent space to the manifold at that point. Tangent bundles are not, in general, trivial bundles: for example, the tangent bundle of the sphere is non-trivial by the hairy ball theorem. In general, a manifold is said to be parallelizable if and only if its tangent bundle is trivial.Vector bundles are almost always required to be locally trivial, however, which means they are examples of fiber bundles. Also, the vector spaces are usually required to be over the real or complex numbers, in which case the vector bundle is said to be a real or complex vector bundle (respectively). Complex vector bundles can be viewed as real vector bundles with additional structure. In the following, we focus on real vector bundles in the category of topological spaces.".
Vector_bundle thumbnail Moebiusstrip.png?width=300.
Vector_bundle wikiPageExternalLink why-is-it-useful-to-classify-the-vector-bundles-of-a-space.
Vector_bundle wikiPageExternalLink why-is-it-useful-to-study-vector-bundles.
Vector_bundle wikiPageExternalLink VBpage.html.
Vector_bundle wikiPageExternalLink smooth.html.
Vector_bundle wikiPageID "276524".
Vector_bundle wikiPageRevisionID "561824114".
Vector_bundle hasPhotoCollection Vector_bundle.
Vector_bundle id "p/v096380".
Vector_bundle title "Vector bundle".
Vector_bundle subject Category:Algebraic_topology.
Vector_bundle subject Category:Differential_topology.
Vector_bundle subject Category:Vector_bundles.
Vector_bundle subject Category:Vectors.
Vector_bundle type Abstraction100002137.
Vector_bundle type Cognition100023271.
Vector_bundle type Collection107951464.
Vector_bundle type Concept105835747.
Vector_bundle type Content105809192.
Vector_bundle type Group100031264.
Vector_bundle type Idea105833840.
Vector_bundle type Package108008017.
Vector_bundle type PsychologicalFeature100023100.
Vector_bundle type Quantity105855125.
Vector_bundle type Variable105857459.
Vector_bundle type Vector105864577.
Vector_bundle type VectorBundles.
Vector_bundle type Vectors.
Vector_bundle comment "In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g.".
Vector_bundle label "Fibrado vectorial".
Vector_bundle label "Fibrado vectorial".
Vector_bundle label "Fibrato vettoriale".
Vector_bundle label "Fibré vectoriel".
Vector_bundle label "Vector bundle".
Vector_bundle label "Vectorbundel".
Vector_bundle label "Vektorbündel".
Vector_bundle label "Wiązka wektorowa".
Vector_bundle label "Векторное расслоение".
Vector_bundle label "حزمة شعاعية".
Vector_bundle label "ベクトル束".
Vector_bundle label "向量丛".
Vector_bundle sameAs Vektorbündel.
Vector_bundle sameAs Fibrado_vectorial.
Vector_bundle sameAs Fibré_vectoriel.
Vector_bundle sameAs Fibrato_vettoriale.
Vector_bundle sameAs ベクトル束.
Vector_bundle sameAs 벡터다발.
Vector_bundle sameAs Vectorbundel.
Vector_bundle sameAs Wiązka_wektorowa.
Vector_bundle sameAs Fibrado_vectorial.
Vector_bundle sameAs m.01pdff.
Vector_bundle sameAs Q658429.
Vector_bundle sameAs Q658429.
Vector_bundle sameAs Vector_bundle.
Vector_bundle wasDerivedFrom Vector_bundle?oldid=561824114.
Vector_bundle depiction Moebiusstrip.png.
Vector_bundle isPrimaryTopicOf Vector_bundle.