  We show that a continuously-normed Banach bundle $\mathcal{E}$ over a compact
Hausdorff space $X$ whose space of sections is algebraically finitely-generated
(f.g.) over $C(X)$ is locally trivial (and hence the section space is
projective f.g over $C(X)$); this answers a question of I. Gogi\'c. As a
preliminary we also provide sufficient conditions for a quotient bundle to be
continuous phrased in terms of the Vietoris continuity of the unit-ball maps
attached to the bundles. Related results include (a) the fact that the category
of topologically f.g. continuous Banach bundles over $X$ is symmetric monoidal
under the (fiber-wise-maximal) tensor product, (b) the full faithfulness of the
global-section functor from topologically f.g. continuous bundles to
$C(X)$-modules and (c) the consequent identification of the algebraically f.g.
bundles as precisely the rigid objects in the aforementioned symmetric monoidal
category.
