Inverse bundle
Encyclopedia
In mathematics, the inverse bundle of a fibre bundle is its inverse with respect to the Whitney sum operation.
Let
be a fibre bundle. A bundle 
is called the inverse bundle of 
if their Whitney sum is a trivial bundle, namely if
Any vector bundle
over a compact
Hausdorff
base has an inverse bundle.
Let
be a fibre bundle. A bundle is called the inverse bundle of if their Whitney sum is a trivial bundle, namely if
Any vector bundle
Vector bundle
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 : to every point x of the space X we associate a vector space V in such a way that these vector spaces fit together...
over a compact
Compact space
In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...
Hausdorff
Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" is the most frequently...
base has an inverse bundle.