The differential geometry of a continuous infinitude of contravariant functional vectors

1. Introduction. - A general theory of function space affinely connected manifolds has been developed by the author in several publications (2). In this paper I propose to give a number of new results pertaining to the differential geometry and invariant theory of a continuous infinitude of contravariant functional vectors. An application is made of these results to the differential geometry of functional group vectors of infinite groups of functional transformations. It is my intention to publish the complete results and proofs elsewhere.