The Weyl bundle as a differentiable manifold

The construction of an infinite-dimensional differentiable manifold R-infinity not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra (P*M-p[[h]], o) and a Weyl algebra bundle (P*M[[h]], o) are presented. Continuity of the o-product in the Tichonov topology is proved. Construction of the *-product of the Fedosov type in terms of theory of connection in a fibre bundle is explained.