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A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.

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Constructing vector bundles of specific stiefel whitney classes?

Is it possible to construct a vector bundle over a given base $X$ such that the $n$th stiefel whitney class vanishes for a given $n?$ What about for some set of integers? Can we make vector bundles o …