Abstract:A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a \text {$\Cal C^\infty $} manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.
Keywords: Colombeau generalized function, distribution, canonical embedding, manifold
AMS Subject Classification: 46F, 46F05