PULLBACKS OF BANACH BUNDLES

Let S and T be compact Hausdorff spaces, alpha : S --> T a continuous map, and rho : F --> T a Banach bundle. The bundle-pi : E --> S which is the pullback to S of rho via alpha, has fibers given by E(p) = F(alpha)(p)) for p is-an-element-of S. The present paper investigates some properties, such as norm continuity and Hausdorfness, which the bundle-pi inherits from rho via the map alpha. The main result presents a relation between the section spaces GAMMA(rho) and GAMMA(pi) via inductive tensor products.