  Construction of an infinite dimensional differentiable manifold ${\mathbb
R}^{\infty}$ not modelled on any Banach space is proposed. Definition, metric
and differential structures of a Weyl algebra and a Weyl algebra bundle are
presented. Continuity of the $\circ$-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.
