Abstract: In this paper, the authors generalize the classical transversality by using the perturbation theory of generalized inverse of linear bounded operator, get the new concept of generalized transversality. The authors also discuss some basic properties of the generalized transversality and the relations between generalized transversality and generalized regular point.

Key words: Banach manifold, Generalized inverse, Generalized transversality, Generalized regualr value, Open set