The word “bundle” recalls an association with a certain set ε divided into nonempty disjoint sets, the fibers. Let ε be the set of all fibers, and let π: ε → β be the mapping that sets the fiber containing a point p ∈ ε in correspondence to this point. The mapping π is uniquely defined by the bundle and in turn uniquely defines this bundle. Moreover, any surjective mapping of the form π: ε → β yields a certain bundle of the set ε (consisting of the inverse images π-1(b) of points b ∈ β). Of course, in the topological case (where ε is a topological space), it is natural to assume that the mapping π is continuous. All this is an explanation and motivation for the following definition.
KeywordsVector Bundle Topological Space Linear Space Tangent Bundle Smooth Manifold
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