 A Banach bundle morphism from the first bundle to the second consists of a pair of morphisms

For "f" to be a morphism means simply that "f" is a continuous map of topological spaces.If the manifolds "M" and "M"′ are both of class "C""p", then the requirement that "f"0 be a morphism is the requirement that it be a "p"-times continuously differentiable function.These two morphisms are required to satisfy two conditions (again, the second one is redundant in the finite-dimensional case)