  Given an arbitrary topological complex vector space $A$, a quotient vector
bundle for $A$ is a quotient of a trivial vector bundle $\pi_2:A\times X\to X$
by a fiberwise linear continuous open surjection. We show that this notion
subsumes that of a Banach bundle over a locally compact Hausdorff space $X$.
Hyperspaces consisting of linear subspaces of $A$, topologized with natural
topologies that include the lower Vietoris topology and the Fell topology,
provide classifying spaces for various classes of quotient vector bundles, in a
way that generalizes the classification of locally trivial vector bundles by
Grassmannians. If $A$ is normed, a finer hyperspace topology is introduced that
classifies bundles with continuous norm, including Banach bundles, and such
that bundles of constant finite rank must be locally trivial.
