Topological characteristics are studied of the set of points at which the stalks of an ample Banach bundle over an extremally disconnected compact space are finite-dimensional or separable. A connection is established between finite dimensionality or separability of the stalks of a bundle and the analogous properties of the stalks of the ample hull of the bundle. A new criterion is obtained for existence of a dual bundle.

Keywords:continuous Banach bundle, ample hull, extremally disconnected compact space, σ-isolated point.