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Remarks on the cohomological classification of certain Frechet bundles

We discuss the classification of certain infinite dimensional fiber bundles mod- elled on Frechet spaces. First we consider vector bundles (over a Banach manifold X) of fiber type a Frechet space , obtained as the limit of a projective system of Banach vector bundles. Such bundles are classified by the cohomology set H 1 (X;H 0 ( )), with coecients in the sheaf of germs of