Bundle
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23-5-2021
1901
Bundle
The term "bundle" is an abbreviated form of the full term fiber bundle. Depending on context, it may mean one of the special cases of fiber bundles, such as a vector bundle or a principal bundle. Bundles are so named because they contain a collection of objects which, like a bundle of hay, are held together in a special way. All of the fibers line up--or at least they line up to nearby fibers.
Locally, a bundle looks like a product manifold in a trivialization. The graph of a function 
sits inside the product as 
. The bundle sections of a bundle generalize functions in this way. It is necessary to use bundles when the range of a function only makes sense locally, as in the case of a vector field on the sphere.
Bundles are a special kind of sheaf.
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